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d of reliability depends on a variety of continuous random variables. 326 NOTE Chapter 5 | Continuous Random Variables The values of discrete and continuous random variables can be ambiguous. For example, if X is equal to the number of miles (to the nearest mile) you drive to work, then X is a discrete random variable.... |
s smiled for more than eight seconds. Find P(x > 12|x > 8) There are two ways to do the problem. For the first way, use the fact that this is a conditional and changes the sample space. The graph illustrates the new sample space. You already know the baby smiled more than eight seconds. for 8 < x < 23 Write a new f(x):... |
splay the value e. The curve is f(x) = 0.25e–0.25x where x is at least zero and m = 0.25. For example, f(5) = 0.25e(−0.25)(5) = 0.072. The probability that the postal clerk spends five minutes with the This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 5 | Continuous Random Variable... |
it would seem to be more likely for a customer to arrive within the next minute. With the exponential This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 5 | Continuous Random Variables 349 distribution, this is not the case—the additional time spent waiting for the next customer do... |
alues generated was 500, not 50. How would that affect what you would expect the empirical data to be and the shape of its graph to look like? 356 Chapter 5 | Continuous Random Variables KEY TERMS conditional probability the likelihood that an event will occur given that another event has already occurred decay paramet... |
bles 363 40. Graph the probability distribution. a. Sketch the graph of the probability distribution. Figure 5.45 Identify the following values: b. i. Lowest value for x¯ : _______ ii. Highest value for x¯ : _______ iii. Height of the rectangle: _______ iv. Label for x-axis (words): _______ v. Label for y-axis (words):... |
o that the time between fireworks is between one and five seconds, and follows a uniform distribution. a. Find the average time between fireworks. b. Find the probability that the time between fireworks is greater than four seconds. 85. The number of miles driven by a truck driver falls between 300 and 700, and follows... |
lecture/lec13.pdf SOLUTIONS 1 Uniform distribution 3 Normal distribution 5 P(6 < x < 7) 7 one 9 zero 11 one 13 0.625 15 The probability is equal to the area from x = 3 2 to x = 4 above the x-axis and up to f(x) = 1 3 . 17 It means that the value of x is just as likely to be any number between 1.5 and 4.5. 19 1.5 ≤ x ≤ ... |
to be more than 0.5? 6.1 | The Standard Normal Distribution The standardized normal distribution is a type of normal distribution, with a mean of 0 and standard deviation of 1. It represents a distribution of standardized scores, called z-scores, as opposed to raw scores (the actual data values). A z-score indicates t... |
nts took the SAT exam. The distribution of scores in the verbal section of the SAT had a mean µ = 496 and a standard deviation σ = 114. Let X = a SAT exam verbal section score in 2012. Then, X ~ N(496, 114). Find the z-scores for x1 = 325 and x2 = 366.21. Interpret each z-score. What can you say about x1 = 325 and x2 =... |
4 d. Find the 70th percentile, —that is, find the score k such that 70 percent of scores are below k and 30 percent of the scores are above k. Solution 6.8 d. Find the 70th percentile. Draw a new graph and label it appropriately. k = 65.6 The 70th percentile is 65.6. This means that 70 percent of the test scores fall a... |
from the section titled Collect the Data give a close approximation to the theoretical distribution in the section titled Analyze the Distribution? In complete sentences and comparing the result in the sections titled Describe the Data and Theoretical Distribution, explain why or why not. 6.4 | Normal Distribution—Pin... |
he left of one in a probability statement? Figure 6.12 44. What is the area to the right of one? Figure 6.13 45. Is P(x < 1) equal to P(x ≤ 1)? Why or why not? 402 Chapter 6 | The Normal Distribution 46. How would you represent the area to the left of three in a probability statement? Figure 6.14 47. What is the area t... |
upervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.5 hours and the amount of time spent alone is normally distributed. We randomly select one Chinese four-year-old living in a rural area. We are interested in the amount of time that child spends a... |
rs. Visually. Retrieved from http://visual.ly/smartphone-users-numbers Statistics Brain Research Institute. http://www.statisticbrain.com/facebook-statistics/ (2013). Facebook company statistics – statistic brain. Retrieved from Wikipedia (2013). Naegele's rule. Retrieved from http://en.wikipedia.org/wiki/Naegele's_rul... |
istributed and ¯ , which consists of sample means, tends ¯ X ∼ N ⎛ ⎝μ x, σ x n ⎞ ⎠ The central limit theorem for sample means says that if you keep drawing larger and larger samples (such as rolling one, two, five, and finally, ten dice) and calculating their means, the sample means form their own normal distribution (... |
ability for the sum (or total of) 80 values. ΣX = the sum or total of 80 values. Because μX = 90, σX = 15, and n = 80, ΣX ~ N[(80)(90), ( 80 )(15)] • mean of the sums = (n)(μX) = (80)(90) = 7200 • • standard deviation of the sums = ( n)(σ X ) = ( 80) (15) sum of 80 values = Σx = 7500 a. Find P(Σx > 7500) P(Σx > 7500) =... |
427 Figure 7.8 REMINDER 1E99 = 1099 and –1E99 = –1099. Press the EE key for E. Or just use 1099 instead of 1E99. ⎛ b. Find P(x > 20). Remember to use the exponential distribution for an individual. X ~ Exp ⎝ ⎞ ⎠ . 1 22 P(x > 20) = e ⎛ ⎝− ⎛ ⎝ 1 22 ⎞ ⎞ ⎠(20) ⎠ ( – 0.04545(20)) or e = 0.4029 c. 1. P(x > 20) = 0.4029, but... |
741 For Part (e), P(X = 175) has normal approximation P(174.5 < Y < 175.5) = 0.0083. normalcdf(174.5,175.5,159,8.6447) = 0.0083 Because of calculators and computer software that let you calculate binomial probabilities for large values of n easily, it is not necessary to use the the normal approximation to the binomial... |
¯ ~ N(μ, σ n ) and ΣΧ ~ N(nμ, ( n )(σ)). If the size (n) of the sample is sufficiently large, then the distribution of the sample means and the distribution of the sample sums will approximate a normal distribution regardless of the shape of the population. The mean of the sample means will equal the population mean, ... |
weight is equally likely, so the distribution of weights is uniform. A sample of 100 weights is taken. 37. a. What is the distribution for the weights of one 25-pound lifting weight? What are the mean and standard deivation? b. What is the distribution for the mean weight of 100 25-pound lifting weights? c. Find the pr... |
each of the 70 managers received a $3,000 raise, graphically, how would that change the distribution in part (b)? 7.3 Using the Central Limit Theorem 76. The attention span of a two-year-old is exponentially distributed with a mean of about eight minutes. Suppose we randomly survey 60 two-year-olds. a. In words, Χ = __... |
18 0.868 0.803 0.932 0.842 0.832 0.807 0.841 0.932 0.833 0.881 0.818 0.864 0.825 0.855 0.942 0.825 0.869 0.912 0.887 Table 7.8 The bag contained 465 candies and the listed weights in the table came from randomly selected candies. Count the weights. a. Find the mean sample weight and the standard deviation of the sample... |
als We use sample data to make generalizations about an unknown population. This part of statistics is called inferential statistics. The sample data help us to make an estimate of a population parameter. We realize that the point estimate is most likely not the exact value of the population parameter, but close to it.... |
standard deviation, σ. • Find the z-score that corresponds to the confidence level. • Calculate the error bound EBM. • Construct the confidence interval. • If we denote the critical z-score by z a 2 , and the sample size by n, then the formula for the confidence interval with confidence level Cl = 1 − α , is given by ... |
s can also be found using appropriate commands on other calculators, using a computer, or using a probability table for the standard normal distribution.) 3 36 ⎞ ⎛ ⎠ = 0.98 EBM = (1.96) ⎝ x¯ – EBM = 68 – 0.98 = 67.02 x¯ + EBM = 68 + 0.98 = 68.98 Notice that the EBM is larger for a 95 percent confidence level in the ori... |
tely separate assumption from normality. Calculators and computers can easily calculate any Student's t-probabilities. The TI-83, 83+, and 84+ have a tcdf function to find the probability for given values of t. The grammar for the tcdf command is tcdf(lower bound, upper bound, degrees of freedom). However, for confiden... |
deviation" is different. For a mean, when the population standard deviation is known, the appropriate standard deviation that we use is σ . For a n proportion, the appropriate standard deviation is pq n . However, in the error bound formula, we use p′ q′ n as the standard deviation, instead of pq n . In the error bound... |
STAT and arrow over to TESTS. Arrow down to A:1-PropZint. Press ENTER. Arrow down to x and enter 15. Arrow down to n and enter 54. Arrow down to C-Level and enter 0.90. Arrow down to Calculate and press ENTER. The confidence interval is (0.178, 0.378). 8.13 The research group referenced in Example 8.13 talked to teens... |
given in Table 8.8 is μ = 63.4. Using the class listing of confidence intervals, count how many of them contain the population mean μ; i.e., for how many intervals does the value of μ lie between the endpoints of the confidence interval? 2. Divide this number by the total number of confidence intervals generated by th... |
oportion of confidence intervals created that is expected to contain the true population parameter Single population mean, known standard deviation, normal distribution Use the normal distribution for means; population standard deviation is known: EBM = z α 2 ⋅ σ n The confidence interval has the format ( x¯ − EBM, x¯ ... |
next 13 exercises: The data in Table 8.10 are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag. X Freq. 1 ... |
onfidence interval for the population mean weight of the candies. i. State the confidence interval. ii. Sketch the graph. iii. Calculate the error bound. f. Construct a 98 percent confidence interval for the population mean weight of the candies. i. State the confidence interval. ii. Sketch the graph. iii. Calculate th... |
9 Table 8.13 Use the sample data to construct a 90 percent confidence interval for the mean age of CEOs for these top small firms. Use the Student's t-distribution. 111. Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its mean number of unoccupied seats per flight o... |
of education in our schools. i. State the confidence interval. ii. Sketch the graph. iii. Calculate the error bound. d. The sampling error given by the group of researchers who conducted the poll is ±3 percent. In one to three complete sentences, explain what the ±3 percent represents. Use the following information to... |
0.2 c. n = 20 ¯ 15 X is the mean weight of a sample of 20 heads of lettuce. 17 EBM = 0.07 CI: (2.1264, 2.2736) 512 Chapter 8 | Confidence Intervals Figure 8.13 19 The interval is greater, because the level of confidence increased. If the only change made in the analysis is a change in confidence level, then all we are ... |
.2)(0.8) 1000 ⎛ ⎝0.2, N . that P′ = 0.2 and n = 1,000, the distribution we should use is c. i. CI: (0.18, 0.22) ii. Check student’s solution. iii. EBM: 0.02 d. One way to lower the sampling error is to increase the sample size. e. The stated ± 3 percent represents the maximum error bound. This means that those doing th... |
mple 527 The Power of the Test is 1 – β. Ideally, we want a high power that is as close to one as possible. Increasing the sample size can increase the Power of the Test. The following are examples of Type I and Type II errors. Example 9.5 Suppose the null hypothesis, H0, is: Frank's rock climbing equipment is safe. Ty... |
bability is called the p-value. When the p-value is very small, it means that the observed test statistic is very unlikely to happen if the null hypothesis is true. This gives significant evidence to suggest that the null hypothesis is false, and to reject it in favor of the alternative hypothesis. In practice, to reje... |
l, the mean time of 16 seconds or less is unlikely to have happened randomly. It is a rare event. Compare α and the p-value: α = 0.05 p-value = 0.0187 α > p-value This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 9 | Hypothesis Testing with One Sample 535 Make a decision: Since α >... |
-value is the probability to the right tail of 1.98 in a t-distribution with nine degrees of freedom. p-value = P( x¯ > 67) = 0.0396 where the sample mean and sample standard deviation are calculated as 67 and 3.1972 from the data. Interpretation of the p-value: If the null hypothesis is true, then there is a 0.0396 pr... |
onfidence interval computation. The poem is clever and humorous, so please enjoy it! Example 9.19 My dog has so many fleas, They do not come off with ease. As for shampoo, I have tried many types Even one called Bubble Hype, Which only killed 25 percent of the fleas, Unfortunately I was not pleased. I've used all kinds... |
to be true is called the null hypothesis (notation H0) and the contradictory statement is called the alternative hypothesis (notation Ha) hypothesis testing based on sample evidence, a procedure for determining whether the hypothesis stated is a reasonable statement and should not be rejected, or is unreasonable and s... |
ould the null and alternative hypotheses be? The distribution of the population is normal. a. H0: ________ b. Ha: ________ 9. A random survey of 75 long-term marathon runners revealed that the mean length of time they've been running is 17.4 years with a standard deviation of 6.3 years. If you were conducting a hypothe... |
. The alternative hypothesis states that the mean is not equal to 88. Is this a left-tailed, right-tailed, or two-tailed test? HOMEWORK 9.1 Null and Alternative Hypotheses 62. Some of the following statements refer to the null hypothesis, some to the alternate hypothesis. State the null hypothesis, H0, and the alternat... |
the variation among prices remains steady with a standard deviation of 20¢. A study was done to test the claim that the mean cost of a daily newspaper is $1.00. Twelve costs yield a mean cost of 95¢ with a standard deviation of 18¢. Do the data support the claim at the 1 percent level? 77. An article in the San Jose M... |
anding Hamlet regarding the latter’s recent experience. Horatio is seated at the large table at right stage. POLONIUS: My Lord, how cans’t thou admit that thou hast seen a ghost! It is but a figment of your imagination! HAMLET: I beg to differ; I know of a certainty that five-and-seventy in one hundred of us, condemned... |
4 months. Conduct a hypothesis test to determine if the mean weaning age in the United States is less than four years old. 103. Harley Davidson motorcycles are the largest selling motorcycle in the United States, with 14 percent of all motorcycles sold in 2012. Interestingly, a random sample of 1,945 stolen motorcycle... |
e picked at random in Times Square visiting the city. 7 a. H0: p = 0.42 b. Ha: p < 0.42 9 a. H0: μ = 15 b. Ha: μ ≠ 15 11 Type I: The mean price of mid-sized cars is $32,000, but we conclude that it is not $32,000. Type II: The mean price of mid-sized cars is not $32,000, but we conclude that it is $32,000. 13 α = the p... |
enever possible. This is beyond the scope of this course. 89 a. H0: μ ≥ 22 b. Ha: μ < 22 c. Let X ¯ = the mean number of bubbles per blow. d. Student's t-distribution e. –2.667 f. p-value = 0.00486 g. Check student’s solution. h. i. Alpha: 0.05 ii. Decision: Reject the null hypothesis. iii. Reason for decision: The p-v... |
two independent population means with unknown and possibly unequal population standard deviations is called the Aspin-Welch t-test. The degrees of freedom formula was developed by Aspin-Welch. The comparison of two population means is very common. A difference between the two samples depends on both the means and the s... |
hypothesis: The means of the final exam scores are equal for the online and face-to- face statistics classes. 2. Ha: μ1 < μ2 Alternative hypothesis: The mean of the final exam scores of the online class is less than the mean of the final exam scores of the face-to-face class. f. left-tailed g. p-value = 0.0011 Figure ... |
t be at least 10 or 20 times the size of the sample. This keeps each population from being over-sampled and causing incorrect results. Comparing two proportions, like comparing two means, is common. If two estimated proportions are different, it may be due to a difference in the populations or it may be due to chance. ... |
indicates less pain. The before value is matched to an after value, and the differences are calculated. The differences have a normal distribution. Are the sensory measurements, on average, lower after the medication? Test at a 5 percent significance level. This OpenStax book is available for free at http://cnx.org/co... |
omplete sentence. 608 Chapter 10 | Hypothesis Testing with Two Samples Decreasing Stocks Survey Randomly pick eight stocks from the newspaper. Using two consecutive days’ business sections, test whether the stocks went down, on average, for the second day. 1. H0: ________ 2. Ha: ________ 3. In words, define the random ... |
0.6. 12. Varsity athletes practice five times a week, on average. 13. A sample of 12 in-state graduate school programs at School A has a mean tuition of $64,000 with a standard deviation of $8,000. At School B, a sample of 16 in-state graduate programs has a mean tuition of $80,000 with a standard deviation of $6,000.... |
of concern. Test at the 1 percent significance level. Patient A B C D E F Before 161 162 165 162 166 171 After 158 159 166 160 167 169 Table 10.23 73. State the null and alternative hypotheses. 74. What is the test statistic? 75. What is the p-value? 76. What is the sample mean difference? 77. What is the conclusion? H... |
me mean amount on texts and supplies each year at their four-year university as they have at their community college. They conducted a random survey of 54 students at their community college and 66 students at their local four-year university. The sample means were $947 and $1,011, respectively. The population standard... |
ith my brothers and sister while we did our daily routine. Every morning, I remember we went to the shamba (garden) to weed our crops. I remember one day arguing with my brother as to why he always remained behind just to join us an hour later. In his defense, he said that he preferred waiting for breakfast before he c... |
use for that test. Left-handed Right-handed Sample size Sample mean 41 97.5 Sample standard deviation 17.5 41 98.1 19.2 Table 10.36 a. Two independent means, normal distribution b. Two independent means, Student’s t-distribution c. Matched or paired samples, Student’s t-distribution d. Two population proportions, norm... |
m variable is the difference in the mean miles per gallon of nonhybrid sedans and hybrid sedans. d. normal e. test statistic: 6.36 f. p-value: 0 g. Check student’s solution. h. i. Alpha: 0.05 ii. Decision: Reject the null hypothesis. iii. Reason for decision: p value < alpha iv. Conclusion: At the 5 percent significanc... |
μ, is located just to the right of the peak. Figure 11.3 11.2 | Goodness-of-Fit Test In this type of hypothesis test, you determine whether the data fit a particular distribution. For example, you may suspect your unknown data fit a binomial distribution. You use a chi-square test, meaning the distribution for the hyp... |
ue, reject Ho. This means you reject the hypothesis that the distribution for the far western states is the same as that of the American population as a whole. Conclusion: At the 1 percent significance level, from the data, there is sufficient evidence to conclude that the number of televisions distribution for the far... |
unity College Students 90.57 115.19 49.24 Four-Year College Students 103 131 56 Nonstudents 104.42 132.81 56.77 Table 11.16 Number of Hours Worked per Week by Volunteer Type (Expected) The table contains expected (E) values (data). For example, the calculation for the expected frequency for the top-left cell is E = (ro... |
and the p-value: α = 0.05 and the p-value = 0.1959. α < p-value. Make a decision: Since α < p-value, do not reject Ho. Conclusion: At a 5 percent level of significance, from the data, there is insufficient evidence to conclude that the distribution of voter preferences was not the same before and after the earthquake.... |
= ________ c. 37th percentile = ________ d. median = ________ e. 63rd percentile = ________ f. 3rd quartile = ________ g. highest value = ________ 3. For each cell, count the observed number of receipts and record it. Then determine the expected number of receipts and record that. Cell Observed Expected 1st 2nd 3rd 4t... |
following information to answer the next nine exercises. The cumulative number of cases of a chronic disease reported for Santa Clara County is broken down by ethnicity as in Table 11.29. Ethnicity White Hispanic Number of Cases 2,229 1,157 Black/African American 457 Asian, Pacific Islander 232 Total = 4,075 Table 11.2... |
Status % Expected Frequency Never Married Married Widowed 31.3% 56.1% 2.5% Divorced/Separated 10.1% Table 11.35 Suppose that a random sample of 400 U.S. males, 18 to 24 years old, yielded the following frequency distribution. We are interested in whether this age group of males fits the distribution of the U.S. adult p... |
ependence. Annual Salary Not a High School Graduate High School Graduate College Graduate Masters or Doctorate < $30,000 15 $30,000–$40,000 20 $40,000–$50,000 10 $50,000–$60,000 5 $60,000+ 0 Table 11.50 25 40 20 10 5 10 70 40 20 10 5 30 55 60 150 This OpenStax book is available for free at http://cnx.org/content/col303... |
mean of $84 and a sample standard deviation of $12, test the claim that the standard deviation is greater than $15. 123. Isabella, an accomplished Bay-to-Breakers runner, claims that the standard deviation for her time to run the 7.5 mile race is at most 3 minutes. To test her claim, Isabella looks up five of her race... |
it the distribution of their expected majors. c. df = 10 d. chi-square distribution with df = 10 e. test statistic = 11.48 f. p-value = 0.3211 g. Check student’s solution. h. i. Alpha = 0.05 ii. Decision: Do not reject null hypothesis when a = 0.05 and a = 0.01. iii. Reason for decision: p-value > alpha iv. Conclusion:... |
tion with one independent variable. The equation has the form y = a + bx where a and b are constant numbers. The variable x is the independent variable; y is the dependent variable. Typically, you choose a value to substitute for the independent variable and then solve for the dependent variable. Example 12.1 The follo... |
s the estimated value of y. It is the value of y obtained using the regression line. It is not generally equal to y from data, but it is still important because it can help make predictions for other values. Figure 12.6 702 Chapter 12 | Linear Regression and Correlation The term y0 – ŷ0 = ε0 is called the error or resi... |
tween x and y (no linear correlation). If r = 1, there is perfect positive correlation. If r = –1, there is perfect negative correlation. In both these cases, all the original data points lie on a straight line. Of course, in the real world, this does not generally happen. What the Sign of r Tells Us • A positive value... |
score (x) and the final exam score (y) because the correlation coefficient is significantly different from zero. Because r is significant and the scatter plot shows a linear trend, the regression line can be used to predict final exam scores. METHOD 2: Using a Table of Critical Values to Make a Decision The 95 Percent... |
carefully what causes a data point to be an outlier. Besides outliers, a sample may contain one or a few points that are called influential points. Influential points are observed data points that are far from the other observed data points in the horizontal direction. These points may have a big effect on the slope of... |
all the |y – ŷ| values are less than 31.29 except for the first one, which is 35: 35 > 31.29. That is, |y – ŷ| ≥ (2)(s). The point that corresponds to |y – ŷ| = 35 is (65, 175). Therefore, the data point (65, 175) is a potential outlier. For this example, we will delete it. (Remember, we do not always delete an outlie... |
uct the line of best fit between two variables. • The student will evaluate the relationship between two variables to determine whether that relationship is significant. Collect the Data Find a reputable source that provides information on total fuel efficiency (in miles per gallon) and weight (in pounds) of new cars w... |
,591 This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 12 | Linear Regression and Correlation 731 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 48,634 59,660 78,530 78,834 71,874 68,505 59,347 47,149 38,393 25,174 25,522 25,643 26,464 31,335 36,560 41,055 44,730 ... |
24 544 363 373 350 741 262 587 327 364 261 Table 12.19 90 86 70 71 65 98 60 87 62 67 50 This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 12 | Linear Regression and Correlation 737 12.4 Prediction (Optional) 61. Recently, the annual numbers of driver deaths per 100,000 people for t... |
onship between the amount of coffee consumed and the heart disease death rate? Carry out an appropriate test at a significance level of 0.05 to help answer this question. 70. The following table consists of one student athlete’s time (in minutes) to swim 2,000 yards and the student’s heart rate (beats per minute) after... |
r free at http://cnx.org/content/col30309/1.8 Chapter 12 | Linear Regression and Correlation 749 78. The following are advertised sale prices of color televisions at Anderson’s: Size (inches) Sale Price ($) 9 20 27 31 35 40 60 Table 12.35 147 197 297 447 1,177 2,177 2,497 a. Decide which variable should be the independ... |
linear relationship between deaths and age. Using the table of critical values for the correlation coefficient, with four degrees of freedom, the critical value is 0.811. The correlation coefficient r = –0.57874 is not less than –0.811, so we do not reject the null hypothesis. f. There is not a linear relationship bet... |
ear relationship. i. There is one outlier (Hawaii). j. rank 51: 75,711.4 square miles, no. 760 k. Chapter 12 | Linear Regression and Correlation Alabama Colorado Hawaii Iowa Maryland Missouri New Jersey Ohio 7 8 6 4 8 8 9 4 1819 1876 1959 1846 1788 1821 1787 1803 South Carolina 13 1788 Utah Wisconsin 4 9 1896 1848 Tabl... |
of Freedom (df) Mean Square (MS) F SS(Factor) SS(Error) SS(Total MS(Factor) = SS(Factor)/(k – 1) F = MS(Factor)/MS(Error) MS(Error) = SS(Error)/(n – k) Factor (Between) Error (Within) Total Table 13.1 Example 13.1 Three different diet plans are to be tested for mean weight loss. The entries in the table are the weight... |
soils in which the bean plants were grown produce the same mean height? Test at a 3 percent level of significance. Solution 13.4 This time, we will perform the calculations that lead to the F' statistic. Notice that each group has the same number of plants, so we will use the formula F' = 2 . n ⋅ s x¯ s2 pooled First,... |
andard deviation For a set of data, a deviation can be represented as x – x¯ where x is a value of the data and x¯ is the sample mean. The sample variance is equal to the sum of the squares of the deviations divided by the difference of the sample size and 1. CHAPTER REVIEW 13.1 One-Way ANOVA Analysis of variance exten... |
commute times are normally distributed. 45. State the null and alternative hypotheses. 46. What is s1 in this problem? 47. What is s2 in this problem? 48. What is n? 49. What is the F statistic? 50. What is the p-value? 51. Is the claim accurate? Use the following information to answer the next four exercises. Two stud... |
. Another was bred to be especially susceptible to DDT (SS). The third group was a control line of nonselected or typical fruit flies (NS). Here are the data: RS SS NS RS SS NS 12.8 38.4 35.4 22.4 23.1 22.6 21.6 32.9 27.4 27.5 29.4 40.4 14.8 48.5 19.3 20.3 16 34.4 23.1 20.9 41.8 38.7 20.1 30.4 34.6 11.6 20.3 26.4 23.3 ... |
ercent level of significance, we do not reject the null hypothesis and state that the data do not show that the variation in drive times for the first worker is less than the variation in drive times for the second worker. 53 2.8674 800 Chapter 13 | F Distribution and One-way Anova 55 Reject the null hypothesis. There ... |
is black given that the student is female. 14. A sample of pounds lost, in a certain month, by individual members of a weight reducing clinic produced the following statistics: • Mean = 5 lbs • Median = 4.5 lbs • Mode = 4 lbs • Standard deviation = 3.8 lbs • First quartile = 2 lbs • Third quartile = 8.5 lbs What is th... |
tudents to graduate is — A. B. C. D. four years four and a half years five years five and a half years 52. Which of the following distributions is described by the following example? Many people can run a short distance of under two miles, but as the distance increases, fewer people can run that far. A. binomial B. uni... |
n the distribution for X. is normal with the same mean but a smaller standard deviation than the distribution for X. 93. The distribution for X is uniform. What can we say for certain about the distribution for ∑ X when n = 50? A. The distribution for ∑ X is still uniform with the same mean and standard deviation as th... |
money altogether would you expect the five customers to spend in one trip to the supermarket in dollars? 128. State the distribution to use if you want to find the probability that the mean amount spent by five customers in one trip to the supermarket is less than $60. Chapter 13 Use the following information to answer... |
ts and calculate each customer’s average spending on produce. 1. Identify the population, sample, parameter, statistic, variable, and data for this example. A. population B. sample C. parameter D. statistic E. variable F. data 2. What kind of data is amount of money spent on produce per visit? A. Qualitative B. Quantit... |
r this data? 2.5: Measures of the Center of the Data 45. In a marathon, the median finishing time was 3:35:04 (three hours, 35 minutes, and four seconds). You finished in 3:34:10. Interpret the meaning of the median time, and discuss your time in relation to it. Use the following information to answer the next three ex... |
gnment, you would have to be able to assign people to either exercise or not exercise. Because exercise has many beneficial effects, this would not be an ethical experiment. We will study people who chose to exercise and compare them to people who chose not to exercise, and try to control for the other ways those two g... |
ajor. 32. What is the probability distribution of X? 33. What is the mean of X? 34. What is the standard deviation of X? 4.5: Hypergeometric Distribution 35. You draw a random sample of 10 students to participate in a survey, from a group of 30, consisting of 16 boys and 14 girls. You are interested in the probability ... |
. 3. The domain of Z = any amount of money from zero upwards. 4. Because they can take any value within their domain, and their value for any particular case is not known until the survey is completed. 5. No, because the domain of Z includes only positive numbers (you cannot spend a negative amount of money). Possibly ... |
mple size increases, the sample mean tends to get nearer and nearer to the population mean. 89. You would expect the mean from a sample of size 100 to be nearer to the population mean, because the law of large numbers says that, as sample size increases, the sample mean tends to approach the population mean. 90. X ~ N(... |
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