The mean height of adult men is 70 inches, with a standard deviation of four inches. The mean height of adult women is 66 inches, with a standard deviation of three inches. Between a man with a height of 74 inches and a woman with a height of 70 inches, who is more unusually tall within his or her respective sex?

Solution: \boxed{The woman, because her height is 1.33 standard deviations above the mean height of all women, whereas the man’s height is only one standard deviation above the mean height of all men.}


Which of the following is not true about t-distributions?

Solution: \boxed{t-distributions always have mean 0 and standard deviation 1.}


To study the effect of alcohol on reaction time, subjects were randomly selected and given three beers to consume. Their reaction time to a simple stimulus was measured before and after drinking the alcohol. Which of the following is a correct statement?

Solution: \boxed{This study was an experiment in which the subjects were used as their own controls.}


Which of these statements correctly explains bias?

Solution: \boxed{It describes a process that creates estimates that are too high on average or too low on average.}


A company that produces facial tissues continually monitors tissue strength. If the mean strength from sample data drops below a specified level, the production process is halted and the machinery inspected. Which of the following would result from a Type I error?

Solution: \boxed{Halting the production process when the tissue strength is within specifications.}


The longevity of people living in a certain locality has a standard deviation of 14 years. What is the mean longevity if 30% of the people live longer than 75 years? Assume a normal distribution for life spans.

Solution: \boxed{75 - 0.5244(14)}


Changing from a 90% confidence interval estimate for a population proportion to a 99% confidence interval estimate, with all other things being equal,

Solution: \boxed{increases the interval size by 57%.}


Which of the following is a binomial random variable?

Solution: \boxed{The number of motorists not wearing seat belts in a random sample of five drivers.}


If all the other variables remain constant, which of the following will increase the power of a hypothesis test? I.Increasing the sample size. II.Increasing the significance level. III.Increasing the probability of a Type II error.

Solution: \boxed{I and II}


Which of the following statements is (are) true? I. In order to use a χ2 procedure, the expected value for each cell of a one- or two-way table must be at least 5. II. In order to use χ2 procedures, you must have at least 2 degrees of freedom. III. In a 4 × 2 two-way table, the number of degrees of freedom is 3.

Solution: \boxed{I and III only}


Suppose two events, E and F, have nonzero probabilities p and q, respectively. Which of the following is impossible?

Solution: \boxed{E and F are both independent and mutually exclusive.}


The probability that there will be an accident on Highway 48 each day depends on the weather. If the weather is dry that day, there is a 0.2% chance of an accident on Highway 48; if the weather is wet that day, there is a 1.0% chance of an accident. Today, the weather station announced that there is a 20% chance of the weather being wet. What is the probability that there will be an accident on Highway 48 today?


The binomial distribution is an appropriate model for which of the following?

Solution: \boxed{None of the above.}


Data were collected on two variables X and Y and a least squares regression line was fitted to the data. The estimated equation for this data is y = –2.29 + 1.70x. One point has x = 5, y = 6. What is the residual for this point?


Which of these explains why t should be used instead of z for inference procedures for means.

Solution: \boxed{When using the sample standard deviation to estimate the population standard deviation, more variability is introduced into the sampling distribution of the statistic.}


Which of the following is least likely to reduce bias in a sample survey?

Solution: \boxed{Using stratified random sampling rather than simple random sampling}


For their first exam, students in an AP Statistics class studied an average of 4 hours with a standard deviation of 1 hour. Almost everyone did poorly on the exam, and so for the second exam every student studied 10 hours. What is the correlation between the numbers of hours students studied for each exam?


The appraised values of houses in a city have a mean of $125,000 with a standard deviation of $23,000. Because of a new teachers' contract, the school district needs an extra 10% in funds compared to the previous year. To raise this additional money, the city instructs the assessment office to raise all appraised house values by $5,000. What will be the new standard deviation of the appraised values of houses in the city?


A large company has offices in two locations, one in New Jersey and one in Utah. The mean salary of office assistants in the New Jersey office is $28,500. The mean salary of office assistants in the Utah office is $22,500. The New Jersey office has 128 office assistants and the Utah office has 32 office assistants. What is the mean salary paid to the office assistants in this company?

Solution: \boxed{$27,300 }


Which of the following is a false statement about simple random samples?

Solution: \boxed{A sample must be reasonably large to be properly considered a simple random sample.}


A telephone executive instructs an associate to contact 104 customers using their service to obtain their opinions in regard to an idea for a new pricing package. The associate notes the number of customers whose names begin with A and uses a random number table to pick four of these names. She then proceeds to use the same procedure for each letter of the alphabet and combines the 4 × 26 = 104 results into a group to be contacted. Which of the following is a correct conclusion?

Solution: \boxed{Her procedure makes use of chance.}


A company has a choice of three investment schemes. Option I gives a sure $25,000 return on investment. Option II gives a 50% chance of returning $50,000 and a 50% chance of returning $10,000. Option III gives a 5% chance of returning $100,000 and a 95% chance of returning nothing. Which option should the company choose?

Solution: \boxed{All of the above answers are correct.}


A one-sided test of a hypothesis about a population mean, based on a sample of size 14, yields a P-value of 0.075. Which of the following best describes the range of tvalues that would have given this P-value?

Solution: \boxed{1.350 < t< 1.771}


The president of an online music streaming service whose customers pay a fee wants to gather additional information about customers who have joined in the past 12 months. The company plans to send out an e-mail survey to a sample of current customers with a link that gives participants a month of streaming service for free once the survey has been completed. They know that musical tastes vary by geographical region. Which of the following sample plans would produce the most representative sample of its customers?

Solution: \boxed{From the list of all customers who joined in the last 12 months, classify customers by the state in which they live, then choose 3% of the customers from each state.}


You need to construct a 94% confidence interval for a population proportion. What is the upper critical value of z to be used in constructing this interval?


A local school has seven math teachers and seven English teachers. When comparing their mean salaries, which of the following is most appropriate?

Solution: \boxed{None of the above are appropriate.}


A small kiosk at the Atlanta airport carries souvenirs in the price range of $3.99 to $29.99, with a mean price of $14.75. The airport authorities decide to increase the rent charged for a kiosk by 5 percent. To make up for the increased rent, the kiosk owner decides to increase the prices of all items by 50 cents. As a result, which of the following will happen?

Solution: \boxed{The mean price will increase by 50 cents, but the standard deviation of prices will remain the same.}


The director of a local food bank asks for data on all donations given during the month of November. Of the 100 checks received, the average donation is $155 with a standard deviation of $32. Which of the following is the most appropriate statement?

Solution: \boxed{This November, the average donation is $155.}


Which of the following describe/s the central limit theorem? I. The mean of the sampling distribution of x-is the same as the mean of the population. II. The standard deviation of the sampling distribution of x-is the same as the standard deviation of x- divided by the square root of the sample size. III. If the sample size is large, the shape of the sampling distribution of x- is approximately normal.

Solution: \boxed{III only}


A large city was interested in annexing part of the surrounding county. In a survey conducted by the local newspaper, 58 percent of respondents said they were against the annexation. During the actual vote, not all eligible voters voted, but 56 percent of the respondents voted against the annexation. Which of the following best describes the difference in the percentages obtained from the newspaper poll and the vote itself?

Solution: \boxed{It is the difference between the same statistics computed from two different samples.}


After receiving several complaints from his customers about the store being closed on Sundays, a storekeeper decided to conduct a survey. He randomly selected 100 female customers and 120 male customers, and asked them, "Are you interested in shopping at this store on Sundays?" He counted the number of customers answering "yes" and constructed a 95 percent confidence interval for the difference by subtracting the proportions of female from the proportion of male customers in favor of shopping on Sundays. The resulting interval was (–0.23, –0.18). Which of the following is a correct interpretation of the interval?

Solution: \boxed{We are 95 percent confident that the proportion of women interested in shopping on Sundays exceeds the proportion of men interested in shopping on Sundays.}


Which of the following is the primary difference between an experiment and an observational study?

Solution: \boxed{Experiments are only conducted on human subjects; observational studies can be conducted on nonhuman subjects.}


Random variable X is normally distributed, with a mean of 25 and a standard deviation of 4. Which of the following is the approximate interquartile range for this distribution?

Solution: \boxed{27.70 – 22.30 = 5.40}


Which of the following statements about any two events A and B is true?

Solution: \boxed{P(A ∩ B) = 0 implies events A and B are mutually exclusive.}


A company has 400 employees. Their mean income is $20,500, and the standard deviation of their incomes is $3,750. The distribution of incomes is normally distributed. How many of the 400 employees do you expect to have an income of between $13,000 and $28,000?


As reported on CNN, in a May 1999 national poll 43% of high school students expressed fear about going to school. Which of the following best describes what is meant by the poll having a margin of error of 5%?

Solution: \boxed{It is likely that the true proportion of high school students afraid to go to school is between 38% and 48%.}


Suppose you wish to compare the AP Statistics exam results for the male and female students taking AP Statistics at your high school. Which is the most appropriate technique for gathering the needed data?

Solution: \boxed{Census}


In one study half of a class were instructed to watch exactly 1 hour of television per day, the other half were told to watch 5 hours per day, and then their class grades were compared. In a second study students in a class responded to a questionnaire asking about their television usage and their class grades.

Solution: \boxed{The first study was an experiment without a control group, while the second was an observational study.}


In a high school of 1650 students, 132 have personal investments in the stock market. To estimate the total stock investment by students in this school, two plans are proposed. Plan I would sample 30 students at random, find a confidence interval estimate of their average investment, and then multiply both ends of this interval by 1650 to get an interval estimate of the total investment. Plan II would sample 30 students at random from among the 132 who have investments in the market, find a confidence interval estimate of their average investment, and then multiply both ends of this interval by 132 to get an interval estimate of the total investment. Which is the better plan for estimating the total stock market investment by students in this school?

Solution: \boxed{Plan II}


Solution: \boxed{because a sample statistic is used to estimate a population parameter.}


The regression analysis of question 20 indicated that "R-sq = 98.1%." Which of the following is (are) true? I. There is a strong positive linear relationship between the explanatory and response variables. II. There is a strong negative linear relationship between the explanatory and response variables. III. About 98% of the variation in the response variable can be explained by the regression on the explanatory variable.

Solution: \boxed{I or II (but not both) and III}


In a clinic, 50 patients with sleep disorders are randomly assigned to one of two different groups. Patients in one group are given medication before bedtime. Patients in the other group are given blindfolds and played soft music at bedtime. Each patient is attached to a machine that records breathing patterns. From the patterns, it is possible to determine if the patient is awake or asleep. The data will be used to decide which method is more effective in helping patients with sleep disorders. Which of the following statements is correct in the context of this experiment?

Solution: \boxed{This is only a single-blind experiment because patients will know which treatment they are receiving, although the examining doctor might not.}


A study was conducted to test a new style of keyboard in preventing repetitive stress disorders. Volunteers who have had problems with such injuries were randomly assigned to use either a traditional keyboard or the new design. A significance test was conducted with the alternative hypothesis that a smaller proportion of those using the new keyboard will suffer injuries than those using the traditional keyboard. The resulting P-value was 0.07. Which is a correct interpretation of this P-value?

Solution: \boxed{There is a 7% chance of getting a difference between the two groups at least as large as the observed difference if the new keyboard is really no better at preventing injuries.}


A college admissions officer is interested in comparing the SAT math scores of high school applicants who have and have not taken AP Statistics. She randomly pulls the files of five applicants who took AP Statistics and five applicants who did not, and proceeds to run a t-test to compare the mean SAT math scores of the two groups. Which of the following is a necessary assumption?

Solution: \boxed{The population of SAT scores from each group is normally distributed.}


Given that P(E) = 0.32, P(F) = 0.15, and P(E ∩ F) = 0.048, which of the following is a correct conclusion?

Solution: \boxed{The events E and F are independent but not mutually exclusive.}


A medical research team tests for tumor reduction in a sample of patients using three different dosages of an experimental cancer drug. Which of the following is true?

Solution: \boxed{There are three levels of a single explanatory variable.}


A department store at a large mall claims that over 60 percent of the mall’s visitors shop at that store. Let p = the proportion of the mall’s visitors who shop at the store. Which of the following pairs of hypotheses should be used to support this claim?

Solution: \boxed{H0: p ≤ 0.60 and Ha: p > 0.60}


Which of the following can affect the value of the correlation r?

Solution: \boxed{None of the above can affect the r value.}


In general, how does tripling the sample size change the confidence interval size?

Solution: \boxed{It divides the interval size by 1.732.}


Suppose the correlation between two variables is r = 0.19. What is the new correlation if 0.23 is added to all values of the x-variable, every value of the y-variable is doubled, and the two variables are interchanged?


Students in AP Statistics class were timed in seconds while solving a series of mathematical brainteasers. One student's time had a standardized score of z = 2.40. If the times are all changed to minutes, what will then be the student's standardized score?

Solution: \boxed{z = 2.40}


An experiment was designed to test the effects of three different types of paint on the durability of wooden toys. Because boys and girls tend to play differently with toys, a randomly selected group of children was divided into two groups by sex. Which of the following statements about this experiment is true?

Solution: \boxed{Sex is a blocking factor.}


Suppose there is a correlation of r = 0.9 between number of hours per day students study and GPAs. Which of the following is a reasonable conclusion?

Solution: \boxed{81% of the variation in GPAs can be explained by variation in number of study hours per day.}


Estrella wants to become a paramedic and takes a screening exam. Scores on the exam have been approximately normally distributed over the years it has been given. The exam is normed with a mean of 80 and a standard deviation of 9. Only those who score in the top 15% on the test are invited back for further evaluation. Estrella received a 90 on the test. What was her percentile rank on the test, and did she qualify for further evaluation?

Solution: \boxed{86.65; she qualified.}


To test whether extensive exercise lowers the resting heart rate, a study is performed by randomly selecting half of a group of volunteers to exercise 1 hour each morning, while the rest are instructed to perform no exercise. Is this study an experiment or an observational study?

Solution: \boxed{None of the above}


Both over-the-counter niacin and the prescription drug Lipitor are known to lower blood cholesterol levels. In one double-blind study Lipitor outperformed niacin. The 95% confidence interval estimate of the difference in mean cholesterol level lowering was (18, 41). Which of the following is a reasonable conclusion?

Solution: \boxed{None of the above.}


Fifty oranges of one variety were selected at random and weighed. A 95 percent confidence interval computed from the sample weights to estimate the mean weight of oranges of this variety is (7.58, 8.72) ounces. Which of the following statements is true with respect to the confidence level used?

Solution: \boxed{In repeated samplings of the same size, 95 percent of the intervals constructed will contain the true mean weight of the oranges of this variety.}


There are two games involving flipping a fair coin. In the first game you win a prize if you can throw between 45% and 55% heads. In the second game you win if you can throw more than 80% heads. For each game would you rather flip the coin 30 times or 300 times?

Solution: \boxed{300 times for the first game and 30 times for the second}


A company is interested in comparing the mean sales revenue per salesperson at two different locations. The manager takes a random sample of 10 salespeople from each location independently and records the sales revenue generated by each person during the last four weeks. He decides to use a t-test to compare the mean sales revenue at the two locations. Which of the following assumptions is necessary for the validity of the t-test?

Solution: \boxed{The population of the sales records at each location is normally distributed.}


Suppose you did 10 independent tests of the form H0: μ = 25 versus Ha: μ < 25, each at the α = 0.05 significance level. What is the probability of committing a Type I error and incorrectly rejecting a true H0 with at least one of the 10 tests?


Suppose that 60% of a particular electronic part last over 3 years, while 70% last less than 6 years. Assuming a normal distribution, what are the mean and standard deviation with regard to length of life of these parts?

Solution: \boxed{μ = 3.977, σ = 3.861}


A psychologist believes that positive rewards for proper behavior are more effective than punishment for bad behavior in promoting good behavior in children. A scale of "proper behavior" is developed. μ1= the "proper behavior" rating for children receiving positive rewards, and μ2= the "proper behavior" rating for children receiving punishment. If H0: μ1− μ2= 0, which of the following is the proper statement of HA?

Solution: \boxed{HA: μ1− μ2> 0}


A confidence interval estimate is determined from the monthly grocery expenditures in a random sample of n families. Which of the following will result in a smaller margin of error? I. A smaller confidence level. II. A smaller sample standard deviation. III. A smaller sample size

Solution: \boxed{I and II}


Which of the following is not important in the design of experiments?

Solution: \boxed{Use of a confounding variable to control the placebo effect}


Which of the following is a correct statement?

Solution: \boxed{When you choose a significance level α, you're setting the probability of a Type I error to exactly α.}


Define a new measurement as the difference between the 60th and 40th percentile scores in a population. This measurement will give information concerning

Solution: \boxed{variability.}


Which of the following is notrequired in a binomial setting?

Solution: \boxed{The value of the random variable of interest is the number of trials until the first success occurs.}


A publisher used standard boxes for shipping books. The mean weight of books packed per box is 25 pounds, with a standard deviation of two pounds. The mean weight of the boxes is one pound, with a standard deviation of 0.15 pounds. The mean weight of the packing material used per box is two pounds, with a standard deviation of 0.25 pounds. What is the standard deviation of the weights of the packed boxes?

Solution: \boxed{2.021 pounds}


A group of scientists wanted to estimate the proportion of geese returning to the same site for the next breeding season. Suppose they decided to increase the sample size from 200 to 2,000. How will this affect the distribution of the sample proportion?

Solution: \boxed{The distribution of the sample proportion will be less spread out.}


A telephone survey of 400 registered voters showed that 256 had not yet made up their minds 1 month before the election. How sure can we be that between 60% and 68% of the electorate were still undecided at that time?


Players in the National Football League weigh, on average, about 248 pounds with a standard deviation of about 47 pounds. If four players are to be selected at random, the expected value of the random variable W, the total combined weight of the four players, is 992 pounds. The standard deviation of Wis approximately

Solution: \boxed{94 pounds}


"A hypothesis test yields a P-value of 0.20." Which of the following best describes what is meant by this statement?

Solution: \boxed{The probability of getting a finding at least as extreme as that obtained by chance alone if the null hypothesis is true is 0.20.}


Which of the following is not true with regard to contingency tables for chi-square tests for independence?

Solution: \boxed{Expected frequencies should be whole numbers.}


The observed times (in minutes) it takes a runner to complete a marathon are normally distributed. The z-score for his running time this week is –2. Which one of the following statements is a correct interpretation of his z-score?

Solution: \boxed{This week his time was two standard deviations lower than his average time.}


The mean Law School Aptitude Test (LSAT) score for applicants to a particular law school is 650 with a standard deviation of 45. Suppose that only applicants with scores above 700 are considered. What percentage of the applicants considered have scores below 740? (Assume the scores are normally distributed.)


On the same test, Mary and Pam scored at the 64th and 56th percentiles, respectively. Which of the following is a true statement?

Solution: \boxed{Eight percent of those who took the test scored between Pam and Mary.}


A study looked at medical records of about 23,000 patients, mostly in Asia. They found that patients who drank at least three cups of green tea per day had a much lower incidence of depression. In an American newspaper article about this study, which of the following statements should not be made?

Solution: \boxed{People who want to avoid depression should consider drinking green tea on a daily basis.}


A researcher planning a survey of school principals in a particular state has lists of the school principals employed in each of the 125 school districts. The procedure is to obtain a random sample of principals from each of the districts rather than grouping all the lists together and obtaining a sample from the entire group. Which of the following is a correct conclusion?

Solution: \boxed{This is a stratified sample, which may give comparative information that a simple random sample wouldn't give.}


In an experiment, the control group should receive

Solution: \boxed{a procedure identical to that given the experimental group except for receiving the treatment under examination.}


Tina’s science fair project was to estimate the mean amount of chemicals in her city’s water supply. At first, she had decided to use a random sample of 15 observations. But her teacher asked her to take 35 observations. The mean and standard deviation from 35 observations turned out to be approximately the same as those from 15 observations. Is there any advantage in using 35 observations instead of 15 observations?

Solution: \boxed{There is some advantage. Because she took 35 observations instead of 15 observations, the confidence interval using 35 observations will be narrower than that using 15 observations.}


The total cholesterol level in a large population of people is strongly skewed right with a mean of 210 mg/dL and a standard deviation of 15 mg/dL. If random samples of size 16 are repeatedly drawn from this population, which of the following appropriately describes the sampling distribution of these sample means?

Solution: \boxed{The shape is somewhat skewed right with a mean of 210 and a standard deviation of 3.75.}


An experiment is conducted in which the response variable is the average gain in participants' performance in the long jump. A two-sample t-test with a 5% level of significance will be used to analyze the results. If all else is kept the same, which of the following descriptions of a possible change in procedure is true?

Solution: \boxed{Taking more careful measurements to reduce variability in the response would increase the power of the test.}


An assembly line machine is supposed to turn out ball bearings with a diameter of 1.25 centimeters. Each morning the first 30 bearings produced are pulled and measured. If their mean diameter is under 1.23 centimeters or over 1.27 centimeters, the machinery is stopped and an engineer is called to make adjustments before production is resumed. The quality control procedure may be viewed as a hypothesis test with the null hypothesis H0: μ = 1.25 and the alternative hypothesis Ha: μ ≠ 1.25. The engineer is asked to make adjustments when the null hypothesis is rejected. In test terminology, what would a Type II error result in?

Solution: \boxed{Continued production of wrong size ball bearings}


We are interested in the proportion p of people who are unemployed in a large city. Eight percent of a simple random sample of 500 people are unemployed. What is the midpoint for a 95% confidence interval estimate of p?

Solution: \boxed{None of the above.}


An insurance company wishes to study the number of years drivers in a large city go between automobile accidents. They plan to obtain and analyze the data from a sample of drivers. Which of the following is a true statement?

Solution: \boxed{None of the above are true statements.}


Which of the following is the central limit theorem?

Solution: \boxed{The central limit theorem refers to something else.}


A manufacturer of ready-bake cake mixes is interested in designing an experiment to test the effects of four different temperature levels (300, 325, 350, and 375F), two different types of pans (glass and metal), and three different types of ovens (gas, electric, and microwave) on the texture of its cakes, in all combinations. Which of the following below is the best description of the design of the necessary experiment?

Solution: \boxed{A completely randomized design with 24 treatment groups}


A study is made to determine whether more hours of academic studying leads to higher point scoring by basketball players. In surveying 50 basketball players, it is noted that the 25 who claim to study the most hours have a higher point average than the 25 who study less. Based on this study, the coach begins requiring the players to spend more time studying. Which of the following is a correct statement?

Solution: \boxed{There could well be a confounding variable responsible for the seeming relationship.}


Biologists around the world have increased efforts at conservation. Monitoring wildlife populations is important so that appropriate management efforts can be implemented, but such monitoring is often difficult. One study found a cheap and easy way to estimate the number of nesting sites of terns (a type of seabird) by monitoring the number of calls heard per minute. More calls happen when there are more birds, as one would expect. In fact, it turned out that the number of calls explained 71% of the variation in the abundance of nests between breeding sites. Which of the following statements is correct about the correlation between the number of calls and the abundance of nests?

Solution: \boxed{The correlation coefficient is 0.84.}


A company has 1000 employees evenly distributed throughout five assembly plants. A sample of 30 employees is to be chosen as follows. Each of the five managers will be asked to place the 200 time cards of their respective employees in a bag, shake them up, and randomly draw out six names. The six names from each plant will be put together to make up the sample. Will this method result in a simple random sample of the 1000 employees?

Solution: \boxed{No, because not every group of 30 employees has the same chance of being selected.}


A doctor hopes that a new surgery technique will shorten the recovery time compared to the standard technique. To test this, he designed an experiment in which patients who required this type of surgery were randomly assigned to the standard technique or the new technique. Then the mean recovery time for each treatment group was compared. Assuming conditions for inference were met, which analysis should be used?

Solution: \boxed{A t-test for a difference in means.}


A researcher plans a study to examine long-term confidence in the U.S. economy among the adult population. She obtains a simple random sample of 30 adults as they leave a Wall Street office building one weekday afternoon. All but two of the adults agree to participate in the survey. Which of the following conclusions is correct?

Solution: \boxed{Selection bias makes this a poorly designed survey.}


To study the effect of music on piecework output at a clothing manufacturer, two experimental treatments are planned: day-long classical music for one group versus day-long light rock music for another. Which one of the following groups would serve best as a control for this study?

Solution: \boxed{A third group for which no music is played}


During the years 1886 through 2000 there were an average of 8.7 tropical cyclones per year, of which an average of 5.1 became hurricanes. Assuming that the probability of any cyclone becoming a hurricane is independent of what happens to any other cyclone, if there are five cyclones in one year, what is the probability that at least three become hurricanes?


A chi-squared test of independence is to be performed on a 3 × 4 contingency table. How many degrees of freedom does this test have?


At a large hospital, the durations of emergency room visits, from check-in to discharge, are approximately normally distributed with a mean of 167 minutes and a standard deviation of 76 minutes. Which interval, to the nearest minute, contains the middle 80% of durations?

Solution: \boxed{70 minutes to 264 minutes}


The relation between studying time (in hours) and grade on a final exam (0-100) in a random sample of students in math class was found to be Grade = 50.25 + 10.2 (h) How will a student’s grade be affected if she studies for two hours?

Solution: \boxed{Her grade will go up by 20.4 points.}


A producer of skin care products has created a new formula for its cream to cure acne. To compare the effectiveness of the new cream to that of the old cream, it conducted a double-blind randomized experiment. Volunteers with acne tried the old formula on one side of their face and the new formula on the other, and which side got which formula was determined randomly. The response variable was the difference in the number of pimples (old formula - new formula). Which is the correct significance test to perform?

Solution: \boxed{A matched pairs t-test}


A pharmaceutical company wants to test a new cholesterol-reducing drug against the previous drug. It does not anticipate much association between cholesterol level and gender, but it does anticipate an association between cholesterol level and the amount of exercise a person gets. For a randomized block design, it should:

Solution: \boxed{Block on exercise level because it is associated with cholesterol level.}


An experiment is to be conducted to determine whether taking fish oil capsules or garlic capsules has more of an effect on cholesterol levels. In past studies it was noted that daily exercise intensity (low, moderate, high) is associated with cholesterol level, but average sleep length (< 5, 5 - 8, > 8 hours) is not associated with cholesterol level. This experiment should be done

Solution: \boxed{by blocking on exercise intensity}


A test for heartworm in dogs shows a positive result in 96% of dogs that actually have heartworm, and shows a negative result in 98% of dogs with no heartworm. If heartworm actually occurs in 10% of dogs, what is the probability that a randomly selected dog that tested positive for heartworm actually has heartworm?


Suppose X and Y are random variables with μx = 32, σx = 5, μy = 44, and σy = 12. Given that X and Y are independent, what are the mean and standard deviation of the random variable X + Y?

Solution: \boxed{μx+y = 76, σx+y = 13}


A high school sent a survey to a randomly selected sample of 75 of last year's graduating class. 27 of those selected did not return the survey. The best plan of action would be to:

Solution: \boxed{Follow up with those that did not return the survey to encourage them to respond.}


Mr. Bee's statistics class had a standard deviation of 11.2 on a standardized test, while Mr. Em's class had a standard deviation of 5.6 on the same test. Which of the following is the most reasonable conclusion concerning the two classes' performance on the test?

Solution: \boxed{Mr. Em's class is more homogeneous than Mr. Bee's.}


When a patient complains to the doctor about a certain set of symptoms, the doctor diagnoses the patient with Condition A 15% of the time. If a patient with these symptoms is diagnosed with Condition A, he or she is diagnosed with Condition B 70% of the time. A patient with these symptoms that is not diagnosed with Condition A is diagnosed with Condition B 10% of the time. What is the probability that a patient with this set of symptoms will be diagnosed with at least one of these conditions?


Solution: \boxed{the method of selection.}


In one study on the effect that eating meat products has on weight level, an SRS of 500 subjects who admitted to eating meat at least once a day had their weights compared with those of an independent SRS of 500 people who claimed to be vegetarians. In a second study, an SRS of 500 subjects were served at least one meat meal per day for 6 months, while an independent SRS of 500 others were chosen to receive a strictly vegetarian diet for 6 months, with weights compared after 6 months.

Solution: \boxed{The first study is an observational study, while the second is a controlled experiment.}


Which of these is a correct description of the term?

Solution: \boxed{Experimental units are the same as subjects.}


In the jury pool available for this week, 30 percent of potential jurors are women. A particular trial requires that, out of a jury of 12, at least three are women. If a jury of 12 is to be selected at random from the pool, what is the probability it meets the requirements of this trial?

Solution: \boxed{The answer cannot be determined without knowing the size of the jury pool.}


An employment placement agency specializes in placing workers in jobs suited for them. From past experience, the agency knows that 20% of all the workers it places will no longer be at the position in which they were placed after one year; however, only 5% of those remaining after the first year leave during the next year. At the start of a year an employer hires 100 workers using this agency, then at the start of the next year the employer hires 100 more. How many of these 200 workers are expected to be on the job at the end of the second year?


A newspaper reporter examined police reports of accidents during the past 12 months to collect data about the speed of a car and its stopping distance. The reporter then constructed a scatterplot and computed a correlation coefficient to show the relation between a car’s speed and its stopping distance. This is an example of

Solution: \boxed{an observational study}


In which of the following situations is a binomial model not an appropriate model to describe the outcome?

Solution: \boxed{The number of rainy days in a given week}


Two possible wordings for a questionnaire on a proposed school budget increase are as follows:

Solution: \boxed{The first showed 58% and the second 13% because of response bias due to the wording of the questions.}


Company I manufactures demolition fuses that burn an average of 50 minutes with a standard deviation of 10 minutes, while company II advertises fuses that burn an average of 55 minutes with a standard deviation of 5 minutes. Which company's fuse is more likely to last at least 1 hour? Assume normal distributions of fuse times.

Solution: \boxed{For both companies, the probability that a fuse will last at least 1 hour is 0.159}


In a random sample of Toyota car owners, 83 out of 112 said they were satisfied with the Toyota front-wheel drive, while in a similar survey of Subaru owners, 76 out of 81 said they were satisfied with the Subaru four-wheel drive. A 90% confidence interval estimate for the difference in proportions between Toyota and Subaru car owners who are satisfied with their drive systems is reported to be -0.197 ± 0.081. Which is a proper conclusion?

Solution: \boxed{We are 90% confident that the difference in proportions between Toyota and Subaru car owners who are satisfied with their drive systems is between -0.278 and -0.116.}


Which of the following statements about the correlation coefficient is true?

Solution: \boxed{Correlations of +0.87 and -0.87 indicate the same degree of clustering around the regression line.}


A school board of a large school district is proposing a new dress code for students. Some students feel that this dress code unfairly targets female students. To see if there is a difference between boys and girls in their opposition to the new dress code, they conduct a poll of 60 randomly selected male and 70 randomly selected female high school students in the district. They find that 66 females oppose the dress code and 50 males oppose the dress code. Which of the following explains why a two-proportion z-test is not appropriate?

Solution: \boxed{The number of successes and the number of failures for the two groups are not all large enough.}


A soft drink dispenser can be adjusted to deliver any fixed number of ounces. If the machine is operating with a standard deviation in delivery equal to 0.3 ounce, what should be the mean setting so that a 12-ounce cup will overflow less than 1% of the time? Assume a normal distribution for ounces delivered.

Solution: \boxed{12 - 2.326(0.3) ounces}


The average number of calories in Yum-Yum Good candy bars is 210, with a standard deviation of 10. If the number of calories per candy bar is normally distributed, what percent of candy bars contain more than 225 calories?


The mean daily demand for bread at a popular bakery is 2,500 loaves, with a standard deviation of 225 loaves. Every morning the bakery bakes 3,000 loaves. What is the probability that today it will run out of bread? Assume that the mean daily demand for bread at this bakery is normally distributed.


Two dice are rolled simultaneously. If both dice show 6, then the player wins $20; otherwise the player loses the game. It costs $2.00 to play the game. What is the expected gain or loss per game?

Solution: \boxed{The player will lose about $1.44.}


Suppose you toss a fair die three times and it comes up an even number each time. Which of the following is a true statement?

Solution: \boxed{The probability that the next toss will again be even is 0.5.}


Taxicabs in a metropolitan area are driven an average of 75,000 miles per year with a standard deviation of 12,000 miles. What is the probability that a randomly selected cab has been driven less than 100,000 miles if it is known that it has been driven over 80,000 miles? Assume a normal distribution of miles per year among cabs.


The registrar’s office at a university has noticed that a large number of students fail to report a change of address. The registrar decides to take a random sample of 150 students from the current directory of students and determine the number of students with the correct addresses on record. He then uses this information to construct a 95 percent confidence interval. Which of the following statements must be true?

Solution: \boxed{The sample proportion of students at this university with the correct address on record is within the confidence interval.}


A botanist is interested in testing H0: μ = 3.5 cm versus Ha: μ > 3.5, where μ = the mean petal length of one variety of flowers. A random sample of 50 petals gives significant results at a 5 percent level of significance. Which of the following statements about the confidence interval to estimate the mean petal length is true?

Solution: \boxed{The specified mean length of 3.5 cm is not within a 90 percent confidence interval.}


A dentist has noticed that about two children in every seven whom he sees professionally develop cavities before they turn 10 years old. Last week he examined the teeth of five unrelated children younger than 10. Let X be the number of children who develop cavities before turning 10. Which of the following gives the probability that at least one will develop a cavity before turning 10?

Solution: \boxed{1 – P(X = 0)}


Which of the following is NOT true of the χ2 probability distribution function?

Solution: \boxed{For the same α, as the number of degrees of freedom increases, the critical value for the rejection region decreases.}


The relation between the selling price of a car (in $1,000) and its age (in years) is estimated from a random sample of cars of a specific model. The relation is given by the following formula: Selling price = 15.9 – 0.983 (age) Which of the following can we conclude from this equation?

Solution: \boxed{For every year the car gets older, the selling price drops by approximately $983.}


Consider a hypothesis test with H0 : μ = 70 and Ha : μ < 70. Which of the following choices of significance level and sample size results in the greatest power of the test when μ = 65?

Solution: \boxed{α = 0.05, n = 30}


A farmer who raises hens for egg production wants his eggs to have a mean mass of 56 grams. He is considering the purchase of a different type of hen, so he took a random sample of 18 eggs laid by this type of hen. The distribution of the masses is symmetric and mound-shaped with a mean of 54.1 grams and no outliers. The farmer conducted a t-test to see if there is evidence that the eggs from these hens have a mean mass that is different from 56 g and got a test statistic of t= -1.973. If he uses a 5% significance level, which is the correct conclusion and reason?

Solution: \boxed{Because tis less extreme than the critical value of t for 17 degrees of freedom, he should not reject the null hypothesis. He does not have convincing evidence at the 5% significance level that the mean mass of eggs from these hens is different from 56 grams.}


A school committee member is lobbying for an increase in the gasoline tax to support the county school system. The local newspaper conducted a survey of county residents to assess their support for such an increase. What is the population of interest here?

Solution: \boxed{All county residents}


To survey the opinions of the students at your high school, a researcher plans to select every twenty-fifth student entering the school in the morning. Assuming there are no absences, will this result in a simple random sample of students attending your school?

Solution: \boxed{No, because not every sample of the intended size has an equal chance of being selected.}


Which of the following is a true statement?

Solution: \boxed{Controlled experiments are often undertaken later to establish cause-and-effect relationships first suggested by observational studies.}


An automobile service station performs oil changes and tire replacements, as well as other services. Sixty percent of its customers request an oil change, 30 percent request tire replacements, and 10 percent request both. A customer requests an oil change. What is the probability this customer does not request tire replacements?


Which of the following statements is false?

Solution: \boxed{The smaller the df, the better the 68-95-99.7 Rule works for t-models.}


A kidney dialysis center periodically checks a sample of its equipment and performs a major recalibration if readings are sufficiently off target. Similarly, a fabric factory periodically checks the sizes of towels coming off an assembly line and halts production if measurements are sufficiently off target. In both situations, we have the null hypothesis that the equipment is performing satisfactorily. For each situation, which is the more serious concern, a Type I or Type II error?

Solution: \boxed{Dialysis center: Type II error, towel manufacturer: Type I error}


A company with offices in five different countries is interested in estimating the proportion of its employees in favor of banning smoking on the office premises. It is known that the views of people from different countries on issues like smoking tend to vary due to the influence of different local social structures. Which of the following is an appropriate sampling technique to use in this situation, and why?

Solution: \boxed{Stratified sample, because the population is divided into five strata—namely, five offices in five different countries}


Semir rolls a six-sided die every morning to determine what he will have for breakfast. If he rolls a 1 or 2, he takes time to cook himself a big breakfast. If he rolls a 3 or larger he grabs a quick lighter breakfast. When he cooks himself a big breakfast, there is a 15% chance he will be late for school. If he has a lighter breakfast, there is a 6% chance he will be late for school. What is the probability Semir will be on time for school any given day?


A teacher's union and a school district are negotiating salaries for the coming year. The teachers want more money, and the district, claiming, as always, budget constraints, wants to pay as little as possible. The district, like most, has a large number of moderately paid teachers and a few highly paid administrators. The salaries of all teachers and administrators are included in trying to figure out, on average, how much the professional staff currently earn. Which of the following would the teachers' union be most likely to quote during negotiations?

Solution: \boxed{The median of all the salaries.}


The Hardcore Construction Company has two offices, one in Atlanta and one in New Orleans. Fifteen engineers work in the Atlanta office, and 14 engineers work in the New Orleans office. The business manager decided to use a 2-sample t-test to compare the mean salaries of engineers in the two offices. Because there were only 15 engineers in one office and 14 engineers in the other, he used the salaries of all the engineers in the computation. Is the 2-sample t-test an appropriate inferential technique in this situation?

Solution: \boxed{No, because the entire population information was used from both offices. Because no samples were taken, a t-test should not be used.}


For the regression line, which of the following statements about residuals is true?

Solution: \boxed{The mean of the residuals is always zero.}


A reading specialist in a large public school system believes that the more time students spend reading, the better they will do in school. She plans a middle school experiment in which an SRS of 30 eighth graders will be assigned four extra hours of reading per week, an SRS of 30 seventh graders will be assigned two extra hours of reading per week, and an SRS of 30 sixth graders with no extra assigned reading will be a control group. After one school year, the mean GPAs from each group will be compared. Is this a good experimental design?

Solution: \boxed{No, because grade level is a lurking variable which may well be confounded with the variables under consideration.}


Solution: \boxed{A distribution of all the values taken by a statistic from all possible samples of a given size}


A farmer wants to know whether a new fertilizer has increased the mean weight of his apples. With the old fertilizer, the mean weight was 4.0 ounces per apple. The farmer decides to test H0: μ = 4.0 ounces versus Ha : μ > 4.0 ounces, at a 5 percent level of significance, where μ = the mean weight of apples using the new fertilizer. The weights of apples are approximately normally distributed. The farmer takes a random sample of 16 apples and computes a mean of 4.3 ounces and a standard deviation of 0.6 ounces. Which of the following gives the p-value for this test?

Solution: \boxed{P(t > 2) with 15 degrees of freedom}


In a study on the effect of music on worker productivity, employees were told that a different genre of background music would be played each day and the corresponding production outputs noted. Every change in music resulted in an increase in production. This is an example of

Solution: \boxed{the placebo effect.}


In a clinical trial, 30 sickle cell anemia patients are randomly assigned to two groups. One group receives the currently marketed medicine, and the other group receives an experimental medicine. Each week, patients report to the clinic where blood tests are conducted. The lab technician is unaware of the kind of medicine the patient is taking. This design can be described as

Solution: \boxed{a completely randomized design, with the currently marketed medicine and the experimental medicine as two treatments}


Suppose that the weights of trucks traveling on the interstate highway system are normally distributed. If 70% of the trucks weigh more than 12,000 pounds and 80% weigh more than 10,000 pounds, what are the mean and standard deviation for the weights of trucks traveling on the interstate system?

Solution: \boxed{μ = 15,300; σ = 6300}


An insurance agent is successful in selling a life insurance policy to 20 percent of the customers he contacts. He decides to construct a simulation to estimate the mean number of customers he needs to contact before being able to sell a policy. Which of the following schemes should he use to do the simulation?

Solution: \boxed{Assign numbers 0, 1 to successfully selling a policy to a customer and numbers 2, 3, 4, 5, 6, 7, 8, 9 to failing to sell a policy to a customer.}


The midterm scores for a statistics course were approximately normally distributed with a mean of 52 points and a standard deviation of 4 points. The final exam scores were approximately normally distributed with a mean of 112 points and a standard deviation of 10 points. One student had a score of 58 points on the midterm. If she had the same standardized score (z-score) on the final exam, what must her score have been?

Solution: \boxed{127 points}


The sampling distribution of the sample mean is close to the normal distribution

Solution: \boxed{if n is large, no matter what the distribution of the original population.}


Suppose H0: p = 0.6, and the power of the test for Ha: p = 0.7 is 0.8. Which of the following is a valid conclusion?

Solution: \boxed{If Ha is true, the probability of failing to reject H0 is 0.2.}


In one metropolitan region, technical writers have an annual salary that is approximately normally distributed with a mean of $55,800. The first quartile of salaries is $48,815. What is the standard deviation?

Solution: \boxed{$10,356 }


The amount of rainfall per month in a certain city is approximately normally distributed, with a mean of six inches and a standard deviation of 1.6 inches. Which of the following is the highest amount of rainfall, in inches, this city could have this month for the month to be among the 10percent driest months the city has seen?


Which of the following is most useful in establishing cause-and-effect relationships?

Solution: \boxed{An experiment}


A sports talk show asks people to call in and give their opinion of the officiating in the local basketball team's most recent loss. What will most likely be the typical reaction?

Solution: \boxed{The team probably wouldn't have lost if the officials had been doing their job.}


Alfred and Ben don't know each other but are each considering asking the lovely Charlene to the school prom. The probability that at least one of them will ask her is 0.72. The probability that they both ask her is 0.18. The probability that Alfred asks her is 0.6. What is the probability that Ben asks Charlene to the prom?


A random sample of 25 men and a separate random sample of 25 women are selected to answer questions about attitudes toward abortion. The answers were categorized as "pro-life" or "pro-choice." Which of the following is the proper null hypothesis for this situation?

Solution: \boxed{The proportion of "pro-life" men is the same as the proportion of "pro-life" women.}


A 2008 survey of 500 households concluded that 82% of the population uses grocery coupons. Which of the following best describes what is meant by the poll having a margin of error of 3%?

Solution: \boxed{It is likely that between 79% and 85% of the population use grocery coupons.}


A hypothesis test is set up so that P(rejecting H0 when H0 is true) = 0.05 and P(failing to reject H0 when H0 is false) = 0.26. What is the power of the test?


For a class project, Charlotte recorded the heights of all 28 students in her class and calculated several statistics. She then realized she made an error recording the height of the tallest person in the class. She correctly had him listed as the tallest, but needed to add two inches to his recorded height to correct it. Which of these measures of spread must remain unchanged?

Solution: \boxed{Interquartile range}


The main purpose of blocking in an experiment is to:

Solution: \boxed{reduce variation within treatments.}


A manufacturer of motor oil is interested in testing the effects of a newly developed additive on the lifespan of an engine. Twenty-five different engine types are selected at random and each one is tested using oil with the additive and oil without the additive. What type of analysis will yield the most useful information?

Solution: \boxed{Matched pairs comparison of population means}


To determine the average cost of running for a congressional seat, a simple random sample of 50 politicians is chosen and the politicians' records examined. The cost figures show a mean of $125,000 with a standard deviation of $32,000. Which of the following is the best interpretation of a 90% confidence interval estimate for the average cost of running for office?

Solution: \boxed{We are 90% confident that politicians running for a congressional seat spend a mean dollar amount between $117,500 and $132,500.}


A filling machine puts an average of four ounces of coffee in jars, with a standard deviation of 0.25 ounces. Forty jars filled by this machine are selected at random. What is the probability that the mean amount per jar filled in the sampled jars is less than 3.9 ounces?


A town has one high school, which buses students from urban, suburban, and rural communities. Which of the following samples is recommended in studying attitudes toward tracking of students in honors, regular, and below-grade classes?

Solution: \boxed{Stratified sample}


A shipment of resistors have an average resistance of 200 ohms with a standard deviation of 5 ohms, and the resistances are normally distributed. Suppose a randomly chosen resistor has a resistance under 194 ohms. What is the probability that its resistance is greater than 188 ohms?


A major polling organization wants to predict the outcome of an upcoming national election (in terms of the proportion of voters who will vote for each candidate). They intend to use a 95% confidence interval with margin of error of no more than 2.5%. What is the minimum sample size needed to accomplish this goal?


Given that the sample has a standard deviation of zero, which of the following is a true statement?

Solution: \boxed{The sample mean and sample median are equal.}


The number of customers served per day by a large department store is normally distributed, with a mean of 3,250 customers and a standard deviation of 320. Find the range of customers served on the middle 50 percent of days.

Solution: \boxed{(3,034, 3,466)}


Suppose that 54% of the graduates from your high school go on to 4-year colleges, 20% go on to 2-year colleges, 19% find employment, and the remaining 7% search for a job. If a randomly selected student is not going on to a 2-year college, what is the probability she will be going on to a 4-year college?


The Department of Health plans to test the lead level in a specific park. Because a high lead level is harmful to children, the park will be closed if the lead level exceeds the allowed limit. The department randomly selects several locations in the park, gets soil samples from those locations, and tests the samples for their lead levels. Which of the following decisions would result from the type I error?

Solution: \boxed{Closing the park when the lead levels are within the allowed limit}


For a class project, a student wants to see if boys and girls at their large high school differ in the number of contacts they have stored in their phone. The student conducts a survey of 50 randomly sampled boys and 40 randomly selected girls, and asks them to report the number of contacts. Which of the following is true about this situation?

Solution: \boxed{Because the shape of the population distribution is not known, the student should notuse a two-sample t-test.}


The probability is 0.2 that a value selected at random from a normal distribution with mean 600 and standard deviation 15 will be above what number?


In a group of 10 scores, the largest score is increased by 40 points. What will happen to the mean?

Solution: \boxed{It will increase by 4 points.}


The distribution of salaries of a county school system with 4,752 employees is known to be right skewed, with the superintendent’s salary an outlier on the higher side. A random sample of 20 employees was taken and their salaries recorded. A 95 percent t-confidence interval for the mean salary of the county school system employees is ($15,360, $32,470). The t-confidence interval is not appropriate in this situation because

Solution: \boxed{the teacher salaries are not negotiable, but the superintendent’s salary is negotiable, so the superintendent’s salary should be excluded from the population sampled}


Assume that the masses of chicken eggs are normally distributed with a mean of 45 g and a standard deviation of 4 g. What mass of egg would be the 25th percentile of the masses of all the eggs?

Solution: \boxed{42.3 g}


A recent poll reported that 43% of Americans approve of the job the president is doing, with a margin of sampling error of ±3.2% at a 95% level of confidence. Which of these correctly interprets that margin of error?

Solution: \boxed{About 95% of polls conducted in this way will give a sample proportion within 3.2 percentage points of the actual proportion of all Americans who approve of the job the president is doing.}


What is the probability of a Type II error when a hypothesis test is being conducted at the 10% significance level (α = 0.10)?

Solution: \boxed{There is insufficient information to answer this question.}


In comparing the life expectancies of two models of refrigerators, the average years before complete breakdown of 10 model A refrigerators is compared with that of 15 model B refrigerators. The 90% confidence interval estimate of the difference is (6, 12). Which of the following is the most reasonable conclusion?

Solution: \boxed{We should be 90% confident that the difference in life expectancies is between 6 and 12 years.}


A medicine is known to produce side effects in one in five patients taking it. Suppose a doctor prescribes the medicine to four unrelated patients. What is the probability that none of the patients will develop side effects?


Which of the following is notan advantage of stratified random sampling over simple random sampling?

Solution: \boxed{When done correctly, a stratified random sample is less biased than a simple random sample.}


In the casino game of roulette, there are 38 slots for a ball to drop into when it is rolled around the rim of a revolving wheel: 18 red, 18 black, and 2 green. What is the probability that the first time a ball drops into the red slot is on the 8th trial (in other words, suppose you are betting on red every time-what is the probability of losing 7 straight times before you win the first time)?


A talk show host recently reported that in response to his on-air question, 82% of the more than 2500 e-mail messages received through his publicized address supported the death penalty for anyone convicted of selling drugs to children. What does this show?

Solution: \boxed{The survey is meaningless because of voluntary response bias.}


To determine the average number of children living in single-family homes, a researcher picks a simple random sample of 50 such homes. However, even after one follow-up visit the interviewer is unable to make contact with anyone in 8 of these homes. Concerned about nonresponse bias, the researcher picks another simple random sample and instructs the interviewer to keep trying until contact is made with someone in a total of 50 homes. The average number of children is determined to be 1.73. Is this estimate probably too low or too high?

Solution: \boxed{Too high, because of undercoverage bias.}


If all the values of a data set are the same, all of the following must equal zero except for which one?

Solution: \boxed{Mean}


A university sent out a survey to a random sample of 120 recent graduates to see how those graduates feel about the education they received. Thirty-two of the graduates did not respond to the survey. Which of these would be the best way to proceed?

Solution: \boxed{Attempt to contact the 32 who did not respond and get the information from them.}


Given the probabilities P(A) = 0.3 and P(B) = 0.2, what is the probability of the union P(A ∪ B) if A and B are mutually exclusive? If A and B are independent? If B is a subset of A?

Solution: \boxed{.5, 0.44, 0.3}


Which of the following is true about any discrete probability distribution of a random variable X?

Solution: \boxed{The probabilities of all possible values of X must add up to one.}


Which among the following would result in the narrowest confidence interval?

Solution: \boxed{Large sample size and 95% confidence}


The correlation between height in inches and weight in pounds for a particular class is 0.65. If the heights are converted from inches to centimeters, what will the correlation be? (1 in. = 2.54 cm)


The number of days it takes to build a new house has a variance of 386. A sample of 40 new homes shows an average building time of 83 days. With what confidence can we assert that the average building time for a new house is between 80 and 90 days?


A significance test of the hypothesis H0: p= 0.3 against the alternative HA: p> 0.3 found a value of = 0.35 for a random sample of size 95. What is the P-value of this test?


Two events A and B each have a nonzero probability. If A and B are independent, which of the following statements is true?

Solution: \boxed{P(A and B) = P(A) · P(B)}


A teacher believes that giving her students a practice quiz every week will motivate them to study harder, leading to a greater overall understanding of the course material. She tries this technique for a year, and everyone in the class achieves a grade of at least C. Is this an experiment or an observational study?

Solution: \boxed{An experiment, but with no reasonable conclusion possible about cause and effect}


Which of these is the best description of a P-value?

Solution: \boxed{The probability of getting a test statistic at least as extreme as the observed test statistic, if the null hypothesis is true.}


The financial aid office at a state university conducts a study to determine the total student costs per semester. All students are charged $4500 for tuition. The mean cost for books is $350 with a standard deviation of $65. The mean outlay for room and board is $2800 with a standard deviation of $380. The mean personal expenditure is $675 with a standard deviation of $125. Assuming independence among categories, what is the standard deviation of the total student costs?


Self-efficacy (the belief that one has control over one's situation) as it related to job satisfaction was studied. When a group of teachers rated their ability to control their situation and their satisfaction with their job, the two variables had a correlation of 0.30. Which statement follows from this correlation?

Solution: \boxed{9% of the variability in job satisfaction can be explained by the linear model with self-efficacy as a predictor.}


Suppose X and Y are random variables with E(X) = 312, var(X) = 6, E(X) = 307, and var(Y) = 8. What are the expected value and variance of the random variable X + Y?


Consider the two sets X = {10, 30, 45, 50, 55, 70, 90} and Y = {10, 30, 35, 50, 65, 70, 90}. Which of the following is false?

Solution: \boxed{None of the above are false.}


Which of the following is a true statement?

Solution: \boxed{None of the above is a true statement.}


A researcher is hoping to find a predictive linear relationship between the explanatory and response variables in her study. Accordingly, as part of her analysis she plans to generate a 95% confidence interval for the slope of the regression line for the two variables. The interval is determined to be (0.45, 0.80). Which of the following is (are) true? (Assume conditions for inference are met.) I. She has good evidence of a linear relationship between the variables. II. It is likely that there is a non-zero correlation (r) between the two variables. III. It is likely that the true slope of the regression line is 0.

Solution: \boxed{I and II only}


A student organization at a university is interested in estimating the proportion of students in favor of showing movies biweekly instead of monthly. How many students should be sampled to get a 90 percent confidence interval with a width of at most 0.08?


A correlation of 0.6 indicates that the percentage of variation in y that is explained by the variation in x is how many times the percentage indicated by a correlation of 0.3?


For which of the following is it appropriate to use a census?

Solution: \boxed{None of the above.}


Which of the following is the best description of the power of a significance test?

Solution: \boxed{The probability of rejecting the null hypothesis if it is, in fact, false.}


A drug company will conduct a randomized controlled study on the effectiveness of a new heart disease medication called Heartaid. Heartaid is more expensive than the currently used medication. The analysis will include a significance test with H0: Heartaid and the current medication are equally effective at preventing heart disease and HA: Heartaid is more effective than the current medication at preventing heart disease. Which of these would be a potential consequence of a Type II error?

Solution: \boxed{Patients will continue to use the current medication, even though Heartaid is actually more effective.}


Two classes take the same exam. Suppose a certain score is at the 40th percentile for the first class and at the 80th percentile for the second class. Which of the following is the most reasonable conclusion?

Solution: \boxed{Students in the first class generally scored higher than students in the second class.}


The mean thrust of a certain model jet engine is 9500 pounds. Concerned that a production process change might have lowered the thrust, an inspector tests a sample of units, calculating a mean of 9350 pounds with a z-score of -2.46 and a P-value of 0.0069. Which of the following is the most reasonable conclusion?

Solution: \boxed{There is evidence to conclude that the new process is producing engines with a mean thrust under 9500 pounds.}


When the point (15,2) is included, the slope of regression line (y= a+ bx) is b= -0.54. The correlation is r= -0.82. When the point is removed, the new slope is -1.04 and the new correlation coefficient is -0.95. What name is given to a point whose removal has this kind of effect on statistical calculations?

Solution: \boxed{Influential point}


Statement 1| Linear regression estimator has the smallest variance among all unbiased estimators. Statement 2| The coefficients α assigned to the classifiers assembled by AdaBoost are always non-negative.

Solution: \boxed{False, True}


Statement 1| RoBERTa pretrains on a corpus that is approximate 10x larger than the corpus BERT pretrained on. Statement 2| ResNeXts in 2018 usually used tanh activation functions.

Solution: \boxed{True, False}


Statement 1| Support vector machines, like logistic regression models, give a probability distribution over the possible labels given an input example. Statement 2| We would expect the support vectors to remain the same in general as we move from a linear kernel to higher order polynomial kernels.

Solution: \boxed{False, False}


A machine learning problem involves four attributes plus a class. The attributes have 3, 2, 2, and 2 possible values each. The class has 3 possible values. How many maximum possible different examples are there?


As of 2020, which architecture is best for classifying high-resolution images?

Solution: \boxed{convolutional networks}


Statement 1| The log-likelihood of the data will always increase through successive iterations of the expectation maximation algorithm. Statement 2| One disadvantage of Q-learning is that it can only be used when the learner has prior knowledge of how its actions affect its environment.

Solution: \boxed{False, False}


Let us say that we have computed the gradient of our cost function and stored it in a vector g. What is the cost of one gradient descent update given the gradient?

Solution: \boxed{O(D)}


Statement 1| For a continuous random variable x and its probability distribution function p(x), it holds that 0 ≤ p(x) ≤ 1 for all x. Statement 2| Decision tree is learned by minimizing information gain.

Solution: \boxed{False, False}


Consider the Bayesian network given below. How many independent parameters are needed for this Bayesian Network H -> U <- P <- W?


As the number of training examples goes to infinity, your model trained on that data will have:

Solution: \boxed{Lower variance}


Statement 1| The set of all rectangles in the 2D plane (which includes non axisaligned rectangles) can shatter a set of 5 points. Statement 2| The VC-dimension of k-Nearest Neighbour classifier when k = 1 is infinite.

Solution: \boxed{True, True}


_ refers to a model that can neither model the training data nor generalize to new data.

Solution: \boxed{underfitting}


Statement 1| The F1 score can be especially useful for datasets with class high imbalance. Statement 2| The area under the ROC curve is one of the main metrics used to assess anomaly detectors.

Solution: \boxed{True, True}


Statement 1| The back-propagation algorithm learns a globally optimal neural network with hidden layers. Statement 2| The VC dimension of a line should be at most 2, since I can find at least one case of 3 points that cannot be shattered by any line.

Solution: \boxed{False, False}


High entropy means that the partitions in classification are

Solution: \boxed{not pure}


Statement 1| Layer Normalization is used in the original ResNet paper, not Batch Normalization. Statement 2| DCGANs use self-attention to stabilize training.

Solution: \boxed{False, False}


In building a linear regression model for a particular data set, you observe the coefficient of one of the features having a relatively high negative value. This suggests that

Solution: \boxed{It is not possible to comment on the importance of this feature without additional information}


For a neural network, which one of these structural assumptions is the one that most affects the trade-off between underfitting (i.e. a high bias model) and overfitting (i.e. a high variance model):

Solution: \boxed{The number of hidden nodes}


For polynomial regression, which one of these structural assumptions is the one that most affects the trade-off between underfitting and overfitting:

Solution: \boxed{The polynomial degree}


Statement 1| As of 2020, some models attain greater than 98% accuracy on CIFAR-10. Statement 2| The original ResNets were not optimized with the Adam optimizer.

Solution: \boxed{True, True}


Solution: \boxed{Minimizes the within class variance for a given number of clusters}


Statement 1| VGGNets have convolutional kernels of smaller width and height than AlexNet's first-layer kernels. Statement 2| Data-dependent weight initialization procedures were introduced before Batch Normalization.

Solution: \boxed{True, True}


What is the rank of the following matrix? A = [[1, 1, 1], [1, 1, 1], [1, 1, 1]]


Statement 1| Density estimation (using say, the kernel density estimator) can be used to perform classification. Statement 2| The correspondence between logistic regression and Gaussian Naive Bayes (with identity class covariances) means that there is a one-to-one correspondence between the parameters of the two classifiers.

Solution: \boxed{True, False}


Suppose we would like to perform clustering on spatial data such as the geometrical locations of houses. We wish to produce clusters of many different sizes and shapes. Which of the following methods is the most appropriate?

Solution: \boxed{Density-based clustering}


Statement 1| In AdaBoost weights of the misclassified examples go up by the same multiplicative factor. Statement 2| In AdaBoost, weighted training error e_t of the tth weak classifier on training data with weights D_t tends to increase as a function of t.

Solution: \boxed{True, True}


MLE estimates are often undesirable because

Solution: \boxed{they have high variance}


Computational complexity of Gradient descent is,

Solution: \boxed{polynomial in D}


Averaging the output of multiple decision trees helps _.

Solution: \boxed{Decrease variance}


The model obtained by applying linear regression on the identified subset of features may differ from the model obtained at the end of the process of identifying the subset during

Solution: \boxed{Forward stage wise selection}


Solution: \boxed{Can use a mix of different activation functions}


Say the incidence of a disease D is about 5 cases per 100 people (i.e., P(D) = 0.05). Let Boolean random variable D mean a patient “has disease D” and let Boolean random variable TP stand for "tests positive." Tests for disease D are known to be very accurate in the sense that the probability of testing positive when you have the disease is 0.99, and the probability of testing negative when you do not have the disease is 0.97. What is P(TP), the prior probability of testing positive.


Statement 1| After mapped into feature space Q through a radial basis kernel function, 1-NN using unweighted Euclidean distance may be able to achieve better classification performance than in original space (though we can’t guarantee this). Statement 2| The VC dimension of a Perceptron is smaller than the VC dimension of a simple linear SVM.

Solution: \boxed{False, False}


Solution: \boxed{It runs reasonably slow for multiple linear regression.}


Predicting the amount of rainfall in a region based on various cues is a ______ problem.

Solution: \boxed{Supervised learning}


Which of the following sentence is FALSE regarding regression?

Solution: \boxed{It discovers causal relationships}


Which one of the following is the main reason for pruning a Decision Tree?

Solution: \boxed{To avoid overfitting the training set}


Statement 1| The kernel density estimator is equivalent to performing kernel regression with the value Yi = 1/n at each point Xi in the original data set. Statement 2| The depth of a learned decision tree can be larger than the number of training examples used to create the tree.

Solution: \boxed{False, False}


Suppose your model is overfitting. Which of the following is NOT a valid way to try and reduce the overfitting?

Solution: \boxed{Improve the optimisation algorithm being used for error minimisation.}


Statement 1| The softmax function is commonly used in mutliclass logistic regression. Statement 2| The temperature of a nonuniform softmax distribution affects its entropy.

Solution: \boxed{True, True}


Which of the following is/are true regarding an SVM?

Solution: \boxed{For two dimensional data points, the separating hyperplane learnt by a linear SVM will be a straight line.}


Which of the following is the joint probability of H, U, P, and W described by the given Bayesian Network H -> U <- P <- W? [note: as the product of the conditional probabilities]

Solution: \boxed{P(H, U, P, W) = P(H) * P(W) * P(P | W) * P(U | H, P)}


Statement 1| Since the VC dimension for an SVM with a Radial Base Kernel is infinite, such an SVM must be worse than an SVM with polynomial kernel which has a finite VC dimension. Statement 2| A two layer neural network with linear activation functions is essentially a weighted combination of linear separators, trained on a given dataset; the boosting algorithm built on linear separators also finds a combination of linear separators, therefore these two algorithms will give the same result.

Solution: \boxed{False, False}


Statement 1| The ID3 algorithm is guaranteed to find the optimal decision tree. Statement 2| Consider a continuous probability distribution with density f() that is nonzero everywhere. The probability of a value x is equal to f(x).

Solution: \boxed{False, False}


Given a Neural Net with N input nodes, no hidden layers, one output node, with Entropy Loss and Sigmoid Activation Functions, which of the following algorithms (with the proper hyper-parameters and initialization) can be used to find the global optimum?

Solution: \boxed{All of the above}


Adding more basis functions in a linear model, pick the most probably option:

Solution: \boxed{Decreases model bias}


Consider the Bayesian network given below. How many independent parameters would we need if we made no assumptions about independence or conditional independence H -> U <- P <- W?


Another term for out-of-distribution detection is?

Solution: \boxed{anomaly detection}


Statement 1| We learn a classifier f by boosting weak learners h. The functional form of f’s decision boundary is the same as h’s, but with different parameters. (e.g., if h was a linear classifier, then f is also a linear classifier). Statement 2| Cross validation can be used to select the number of iterations in boosting; this procedure may help reduce overfitting.

Solution: \boxed{False, True}


Statement 1| Highway networks were introduced after ResNets and eschew max pooling in favor of convolutions. Statement 2| DenseNets usually cost more memory than ResNets.

Solution: \boxed{False, True}


If N is the number of instances in the training dataset, nearest neighbors has a classification run time of

Solution: \boxed{O( N )}


Statement 1| The original ResNets and Transformers are feedforward neural networks. Statement 2| The original Transformers use self-attention, but the original ResNet does not.

Solution: \boxed{True, True}


Statement 1| RELUs are not monotonic, but sigmoids are monotonic. Statement 2| Neural networks trained with gradient descent with high probability converge to the global optimum.

Solution: \boxed{False, True}


The numerical output of a sigmoid node in a neural network:

Solution: \boxed{Is bounded between 0 and 1.}


Which of the following can only be used when training data are linearly separable?

Solution: \boxed{Linear hard-margin SVM.}


Which of the following are the spatial clustering algorithms?

Solution: \boxed{All of the above}


Statement 1| The maximum margin decision boundaries that support vector machines construct have the lowest generalization error among all linear classifiers. Statement 2| Any decision boundary that we get from a generative model with classconditional Gaussian distributions could in principle be reproduced with an SVM and a polynomial kernel of degree less than or equal to three.

Solution: \boxed{False, True}


Statement 1| L2 regularization of linear models tends to make models more sparse than L1 regularization. Statement 2| Residual connections can be found in ResNets and Transformers.

Solution: \boxed{False, True}


Suppose we like to calculate P(H|E, F) and we have no conditional independence information. Which of the following sets of numbers are sufficient for the calculation?

Solution: \boxed{P(E, F), P(H), P(E, F|H)}


Which among the following prevents overfitting when we perform bagging?

Solution: \boxed{The use of weak classifiers}


Statement 1| PCA and Spectral Clustering (such as Andrew Ng’s) perform eigendecomposition on two different matrices. However, the size of these two matrices are the same. Statement 2| Since classification is a special case of regression, logistic regression is a special case of linear regression.

Solution: \boxed{False, False}


Statement 1| The Stanford Sentiment Treebank contained movie reviews, not book reviews. Statement 2| The Penn Treebank has been used for language modeling.

Solution: \boxed{True, True}


What is the dimensionality of the null space of the following matrix? A = [[3, 2, −9], [−6, −4, 18], [12, 8, −36]]


Solution: \boxed{The only examples necessary to compute f(x) in an SVM.}


Statement 1| Word2Vec parameters were not initialized using a Restricted Boltzman Machine. Statement 2| The tanh function is a nonlinear activation function.

Solution: \boxed{True, True}


If your training loss increases with number of epochs, which of the following could be a possible issue with the learning process?

Solution: \boxed{Step size is too large}


Say the incidence of a disease D is about 5 cases per 100 people (i.e., P(D) = 0.05). Let Boolean random variable D mean a patient “has disease D” and let Boolean random variable TP stand for "tests positive." Tests for disease D are known to be very accurate in the sense that the probability of testing positive when you have the disease is 0.99, and the probability of testing negative when you do not have the disease is 0.97. What is P(D | TP), the posterior probability that you have disease D when the test is positive?


Statement 1| Traditional machine learning results assume that the train and test sets are independent and identically distributed. Statement 2| In 2017, COCO models were usually pretrained on ImageNet.

Solution: \boxed{True, True}


Statement 1| The values of the margins obtained by two different kernels K1(x, x0) and K2(x, x0) on the same training set do not tell us which classifier will perform better on the test set. Statement 2| The activation function of BERT is the GELU.

Solution: \boxed{True, True}


Which of the following is a clustering algorithm in machine learning?

Solution: \boxed{Expectation Maximization}


You've just finished training a decision tree for spam classification, and it is getting abnormally bad performance on both your training and test sets. You know that your implementation has no bugs, so what could be causing the problem?

Solution: \boxed{Your decision trees are too shallow.}


Solution: \boxed{linear in K}


Statement 1| Industrial-scale neural networks are normally trained on CPUs, not GPUs. Statement 2| The ResNet-50 model has over 1 billion parameters.

Solution: \boxed{False, False}


Given two Boolean random variables, A and B, where P(A) = 1/2, P(B) = 1/3, and P(A | ¬B) = 1/4, what is P(A | B)?


Existential risks posed by AI are most commonly associated with which of the following professors?

Solution: \boxed{Stuart Russell}


Statement 1| Maximizing the likelihood of logistic regression model yields multiple local optimums. Statement 2| No classifier can do better than a naive Bayes classifier if the distribution of the data is known.

Solution: \boxed{False, False}


For Kernel Regression, which one of these structural assumptions is the one that most affects the trade-off between underfitting and overfitting:

Solution: \boxed{The kernel width}


Statement 1| The SVM learning algorithm is guaranteed to find the globally optimal hypothesis with respect to its object function. Statement 2| After being mapped into feature space Q through a radial basis kernel function, a Perceptron may be able to achieve better classification performance than in its original space (though we can’t guarantee this).

Solution: \boxed{True, True}


For a Gaussian Bayes classifier, which one of these structural assumptions is the one that most affects the trade-off between underfitting and overfitting:

Solution: \boxed{Whether we assume full class covariance matrices or diagonal class covariance matrices}


Statement 1| Overfitting is more likely when the set of training data is small. Statement 2| Overfitting is more likely when the hypothesis space is small.

Solution: \boxed{False, True}


Statement 1| Besides EM, gradient descent can be used to perform inference or learning on Gaussian mixture model. Statement 2 | Assuming a fixed number of attributes, a Gaussian-based Bayes optimal classifier can be learned in time linear in the number of records in the dataset.

Solution: \boxed{True, True}


Statement 1| In a Bayesian network, the inference results of the junction tree algorithm are the same as the inference results of variable elimination. Statement 2| If two random variable X and Y are conditionally independent given another random variable Z, then in the corresponding Bayesian network, the nodes for X and Y are d-separated given Z.

Solution: \boxed{True, False}


Given a large dataset of medical records from patients suffering from heart disease, try to learn whether there might be different clusters of such patients for which we might tailor separate treatments. What kind of learning problem is this?

Solution: \boxed{Unsupervised learning}


What would you do in PCA to get the same projection as SVD?

Solution: \boxed{Transform data to zero mean}


Statement 1| The training error of 1-nearest neighbor classifier is 0. Statement 2| As the number of data points grows to infinity, the MAP estimate approaches the MLE estimate for all possible priors. In other words, given enough data, the choice of prior is irrelevant.

Solution: \boxed{True, False}


When doing least-squares regression with regularisation (assuming that the optimisation can be done exactly), increasing the value of the regularisation parameter λ the testing error.

Solution: \boxed{will never decrease the training error.}


Which of the following best describes what discriminative approaches try to model? (w are the parameters in the model)

Solution: \boxed{p(y|x, w)}


Statement 1| CIFAR-10 classification performance for convolution neural networks can exceed 95%. Statement 2| Ensembles of neural networks do not improve classification accuracy since the representations they learn are highly correlated.

Solution: \boxed{True, False}


Which of the following points would Bayesians and frequentists disagree on?

Solution: \boxed{The use of prior distributions on the parameters in a probabilistic model.}


Statement 1| The BLEU metric uses precision, while the ROGUE metric uses recall. Statement 2| Hidden markov models were frequently used to model English sentences.

Solution: \boxed{True, True}


Statement 1| ImageNet has images of various resolutions. Statement 2| Caltech-101 has more images than ImageNet.

Solution: \boxed{True, False}


Which of the following is more appropriate to do feature selection?

Solution: \boxed{Lasso}


Suppose you are given an EM algorithm that finds maximum likelihood estimates for a model with latent variables. You are asked to modify the algorithm so that it finds MAP estimates instead. Which step or steps do you need to modify?

Solution: \boxed{Maximization}


Statement 1| For any two variables x and y having joint distribution p(x, y), we always have H[x, y] ≥ H[x] + H[y] where H is entropy function. Statement 2| For some directed graphs, moralization decreases the number of edges present in the graph.

Solution: \boxed{False, False}


Which of the following is NOT supervised learning?

Solution: \boxed{PCA}


Statement 1| A neural network's convergence depends on the learning rate. Statement 2| Dropout multiplies randomly chosen activation values by zero.

Solution: \boxed{True, True}


Which one of the following is equal to P(A, B, C) given Boolean random variables A, B and C, and no independence or conditional independence assumptions between any of them?

Solution: \boxed{P(A, B | C) * P(C)}


Which of the following tasks can be best solved using Clustering.

Solution: \boxed{Detecting fraudulent credit card transactions}


After applying a regularization penalty in linear regression, you find that some of the coefficients of w are zeroed out. Which of the following penalties might have been used?

Solution: \boxed{either (a) or (b)}


A and B are two events. If P(A, B) decreases while P(A) increases, which of the following is true?

Solution: \boxed{P(B|A) decreases}


Statement 1| When learning an HMM for a fixed set of observations, assume we do not know the true number of hidden states (which is often the case), we can always increase the training data likelihood by permitting more hidden states. Statement 2| Collaborative filtering is often a useful model for modeling users' movie preference.

Solution: \boxed{True, True}


You are training a linear regression model for a simple estimation task, and notice that the model is overfitting to the data. You decide to add in $\ell_2$ regularization to penalize the weights. As you increase the $\ell_2$ regularization coefficient, what will happen to the bias and variance of the model?

Solution: \boxed{Bias increase ; Variance decrease}


Which PyTorch 1.8 command(s) produce $10\times 5$ Gaussian matrix with each entry i.i.d. sampled from $\mathcal{N}(\mu=5,\sigma^2=16)$ and a $10\times 10$ uniform matrix with each entry i.i.d. sampled from $U[-1,1)$?

Solution: \boxed{\texttt{5 + torch.randn(10,5) * 4} ; \texttt{2 * torch.rand(10,10) - 1}}


Statement 1| The ReLU's gradient is zero for $x<0$, and the sigmoid gradient $\sigma(x)(1-\sigma(x))\le \frac{1}{4}$ for all $x$. Statement 2| The sigmoid has a continuous gradient and the ReLU has a discontinuous gradient.

Solution: \boxed{True, True}


Which is true about Batch Normalization?

Solution: \boxed{The bias parameter of affine layers becomes redundant if a batch normalization layer follows immediately afterward.}


Suppose we have the following objective function: $\argmin_{w} \frac{1}{2} \norm{Xw-y}^2_2 + \frac{1}{2}\gamma \norm{w}^2_2$ What is the gradient of $\frac{1}{2} \norm{Xw-y}^2_2 + \frac{1}{2}\lambda \norm{w}^2_2$ with respect to $w$?

Solution: \boxed{$\nabla_w f(w) = X^\top X w - X^\top y + \lambda w$}


Which of the following is true of a convolution kernel?

Solution: \boxed{Convolving an image with $\begin{bmatrix}0 & 0 & 0\\ 0 & 1 & 0 \\ 0 & 0 & 0 \end{bmatrix}$ would not change the image}


Solution: \boxed{A bounding box with an IoU (intersection over union) equal to $3\%$ would likely be considered at false negative.}


Solution: \boxed{A combination of ReLUs such as $ReLU(x) - ReLU(x-1)$ is convex.}


We are training fully connected network with two hidden layers to predict housing prices. Inputs are $100$-dimensional, and have several features such as the number of square feet, the median family income, etc. The first hidden layer has $1000$ activations. The second hidden layer has $10$ activations. The output is a scalar representing the house price. Assuming a vanilla network with affine transformations and with no batch normalization and no learnable parameters in the activation function, how many parameters does this network have?


Statement 1| The derivative of the sigmoid $\sigma(x)=(1+e^{-x})^{-1}$ with respect to $x$ is equal to $\text{Var}(B)$ where $B\sim \text{Bern}(\sigma(x))$ is a Bernoulli random variable. Statement 2| Setting the bias parameters in each layer of neural network to 0 changes the bias-variance trade-off such that the model's variance increases and the model's bias decreases

Solution: \boxed{True, False}