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st the restaurants in the sample you obtained. NOTE The following section contains restaurants stratified by city into columns and grouped horizontally by entree cost (clusters). Restaurants Stratified by City and Entree Cost Entree Cost San Jose Under $10 $10 to under $15 $15 to under $20 Over $20 El Abuelo Taq, Pasta... |
d. If necessary, return to the beginning of the population list to complete your sample. Treatments different values or components of the explanatory variable applied in an experiment Variable a characteristic of interest for each person or object in a population CHAPTER REVIEW 1.1 Definitions of Statistics, Probabilit... |
2. Suppose that the first researcher conducted his survey by randomly choosing one state in the nation and then randomly picking 40 patients from that state. What sampling method would that researcher have used? 23. Suppose that the second researcher conducted his survey by choosing 40 patients he knew. What sampling m... |
getting accurate results from a telephone survey. 69. List some practical difficulties involved in getting accurate results from a mailed survey. 70. With your classmates, brainstorm some ways you could overcome these problems if you needed to conduct a phone or mail survey. 71. The instructor takes her sample by gath... |
ved at the incorrect number(s). b. Explain what is wrong with this statement: “47 percent of the people surveyed have lived in the U.S. for 5 years.” c. Fix the statement in b to make it correct. d. What fraction of the people surveyed have lived in the U.S. five or seven years? e. What fraction of the people surveyed ... |
l, Jan no. 50 (2013), http://www.ncbi.nlm.nih.gov/pubmed/22721550 (accessed May 1, 2013). “Earthquake Information by Year,” U.S. Geological Survey. http://earthquake.usgs.gov/earthquakes/eqarchives/year/ (accessed May 1, 2013). “Fatality Analysis Report Systems (FARS) Encyclopedia,” National Highway Traffic and Safety ... |
, but his sample would not detect such results. He also looked only at the most popular textbook in each of the subjects he investigated. The availability of the most popular textbooks may differ from the availability of other textbooks in one of two ways: • • the most popular textbooks may be more readily available on... |
is (horizontal axis) consists of data values and the y-axis (vertical axis) consists of frequency points. The frequency points are connected using line segments. This content is available for free at http://textbookequity.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 CHAPTER 2 | DESCRIPTIVE STA... |
oductory-statistics or at http://cnx.org/content/col11562/1.16 CHAPTER 2 | DESCRIPTIVE STATISTICS 79 5; 5; 5; 5; 5 6; 6 Eleven students buy one book. Ten students buy two books. Sixteen students buy three books. Six students buy four books. Five students buy five books. Two students buy six books. Because the data are ... |
Emissions Ukraine United Kingdom United States 2003 352,259 2004 343,121 2005 339,029 2006 327,797 2007 328,357 2008 323,657 2009 272,176 Table 2.20 540,640 540,409 541,990 542,045 528,631 522,247 474,579 5,681,664 5,790,761 5,826,394 5,737,615 5,828,697 5,656,839 5,299,563 Uses of a Time Series Graph Time series graph... |
n the table (between the 40th and 41st values). Therefore, we need to take the mean of the 40th an 41st values. The 80th percentile = 8 + 9 2 = 8.5 b. The 90th percentile will be the 45th data value (location is 0.90(50) = 45) and the 45th data value is nine. c. Q1 is also the 25th percentile. The 25th percentile locat... |
rtile, the median, the third quartile, and the maximum value. We use these values to compare how close other data values are to them. To construct a box plot, use a horizontal or vertical number line and a rectangular box. The smallest and largest data values label the endpoints of the axis. The first quartile marks on... |
dle value of the ordered data (ordered smallest to largest). If n is an even number, the median is equal to the two middle values added together and divided by two after the data has been ordered. For example, if the total number of data values is 97, then n + 1 = 49. The median is the 49th value in the ordered data. I... |
quity.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 CHAPTER 2 | DESCRIPTIVE STATISTICS 105 Figure 2.18 The mean is 7.7, the median is 7.5, and the mode is seven. Of the three statistics, the mean is the largest, while the mode is the smallest. Again, the mean reflects the skewing the most. To s... |
calculator, you need to select the appropriate standard deviation σx or sx from the summary statistics. We will concentrate on using and interpreting the information that the standard deviation gives us. However you should study the following step-by-step example to help you understand how 110 CHAPTER 2 | DESCRIPTIVE S... |
l value of the data with precision. In other words, we cannot find the exact mean, median, or mode. We can, however, determine the best estimate of ∑ f m ∑ f the measures of center by finding the mean of the grouped data with the formula: Mean o f Frequency Table = where f = interval frequencies and m = interval midpoi... |
ay not be part of the data. The second quartile is the median of the data. Relative Frequency the ratio of the number of times a value of the data occurs in the set of all outcomes to the number of all outcomes Skewed used to describe data that is not symmetrical; when the right side of a graph looks “chopped off” comp... |
ence competition supplied in Exercise 2.10. Construct a bar graph that shows the county-wide population percentage of students at each school. 2.2 Histograms, Frequency Polygons, and Time Series Graphs 12. Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourt... |
lowing: 46. sample mean = x¯ = _______ 47. median = _______ 48. mode = _______ 2.6 Skewness and the Mean, Median, and Mode Use the following information to answer the next three exercises: State whether the data are symmetrical, skewed to the left, or skewed to the right. 49. 1; 1; 1; 2; 2; 2; 2; 3; 3; 3; 3; 3; 3; 3; 3... |
able 2.68 Percent (%) State Percent (%) State Percent (%) 32.2 24.5 24.3 30.1 24.0 21.0 22.5 28.0 Kentucky Louisiana Maine Maryland 31.3 31.0 26.8 27.1 North Dakota 27.2 Ohio Oklahoma Oregon 29.2 30.4 26.8 Massachusetts 23.0 Pennsylvania 28.6 Michigan Minnesota Mississippi 30.9 24.8 34.0 Rhode Island 25.5 South Carolin... |
nstruments of the same type. Justify your answer. 105. An elementary school class ran one mile with a mean of 11 minutes and a standard deviation of three minutes. Rachel, a student in the class, ran one mile in eight minutes. A junior high school class ran one mile with a mean of nine minutes and a standard deviation ... |
| DESCRIPTIVE STATISTICS 122. Suppose that a publisher conducted a survey asking adult consumers the number of fiction paperback books they had purchased in the previous month. The results are summarized in the Table 2.83. # of books Freq. Rel. Freq. 0 1 2 3 4 5 7 9 Table 2.83 18 24 24 22 15 10 5 1 a. Are there any ou... |
re {Arkansas, Washington DC, Idaho, Maryland, Michigan, Mississippi, Virginia, Wyoming}. This content is available for free at http://textbookequity.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 Corresponding percents are {30.1, 22.2, 26.5, 27.1, 30.9, 34.0, 26.0, 25.1}. CHAPTER 2 | DESCRIPTIVE... |
data as estimates of the following probabilities. P(change) means the probability that a randomly chosen person in your class has change in his/her pocket or purse. P(bus) means the probability that a randomly chosen person in your class rode a bus within the last month and so on. Discuss your answers. • Find P(change... |
. e. A GIVEN B f. B GIVEN A g. A AND B h. A OR B This content is available for free at http://textbookequity.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 CHAPTER 3 | PROBABILITY TOPICS 167 i. A OR B′ j. Event N = the outcome is a prime number. k. Event I = the outcome is seven. Solution 3.2 a.... |
two balls of different colors. c. Let H = the event of getting white on the first pick. d. Are F and G mutually exclusive? e. Are G and H mutually exclusive? Example 3.8 Roll one fair, six-sided die. The sample space is {1, 2, 3, 4, 5, 6}. Let event A = a face is odd. Then A = {1, 3, 5}. Let event B = a face is even. T... |
A AND B). If A and B are mutually exclusive, then P(A AND B) = 0. Then P(A OR B) = P(A) + P(B) - P(A AND B) becomes P(A OR B) = P(A) + P(B). Example 3.14 Klaus is trying to choose where to go on vacation. His two choices are: A = New Zealand and B = Alaska • Klaus can only afford one vacation. The probability that he c... |
before exercising and how many had injuries within the past year. Injury in last year No injury in last year Total Stretches 55 Does not stretch 231 Total 286 Table 3.3 295 219 514 350 450 800 a. What is P(athlete stretches before exercising)? b. What is P(athlete stretches before exercising|no injury in the last year... |
k or replace the first marble after you have drawn it. You draw without replacement, so that on the second draw there are ten marbles left in the urn. Calculate the following probabilities using the tree diagram. a. P(RR) = ________ Solution 3.25 a. P(RR) = ⎛ 3 ⎝ 11 ⎛ ⎞ ⎠ ⎝ 2 10 ⎞ ⎠ = 6 110 b. Fill in the blanks: P(RB ... |
eplacement” probabilities different? 2. Convert P(no yellows) to decimal format for both Theoretical “With Replacement” and for Empirical “With Replacement”. Round to four decimal places. a. Theoretical “With Replacement”: P(no yellows) = _______ b. Empirical “With Replacement”: P(no yellows) = _______ c. Are the decim... |
try is in North America. Let O = the event that a country is in Oceania. Let S = the event that a country is in South America. 12. Find P(A). 13. Find P(E). This content is available for free at http://textbookequity.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 CHAPTER 3 | PROBABILITY TOPICS 2... |
is more than 81? 71. Find the probability that an Emotional Health Index Score is between 80.5 and 82? 72. If we know an Emotional Health Index Score is 81.5 or more, what is the probability that it is 82.7? 73. What is the probability that an Emotional Health Index Score is 80.7 or 82.7? 74. What is the probability th... |
y statement for the percent of money returned out of the economics classes. c. Write a probability statement for the percent of money returned out of the other classes. d. e. Based upon this study, do you think that economists are more selfish than other people? Explain why or why not. Is money being returned independe... |
okequity.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 CHAPTER 3 | PROBABILITY TOPICS 213 Shirt# ≤ 210 211–250 251–290 290≤ 1–33 21 34–66 66–99 6 6 Table 3.24 5 18 12 0 7 22 0 4 5 For the following, suppose that you randomly select one player from the 49ers or Cowboys. If having a shirt number ... |
Society. Data from The Data and Story Library, 1996. Available online at http://lib.stat.cmu.edu/DASL/ (accessed May 2, 2013). Data from the Federal Highway Administration, part of the United States Department of Transportation. Data from the United States Census Bureau, part of the United States Department of Commerce... |
nd understand discrete probability distribution functions, in general. • Calculate and interpret expected values. • Recognize the binomial probability distribution and apply it appropriately. • Recognize the Poisson probability distribution and apply it appropriately. • Recognize the geometric probability distribution ... |
nurse during a 12-hour shift. For a random sample of 50 patients, the following information was obtained. What is the expected value? x P(x) 0 1 2 3 4 5 P(x = 0) = 4 50 P(x = 1) = 8 50 P(x = 2) = 16 50 P(x = 3) = 14 50 P(x = 4) = 6 50 P(x = 5) = 2 50 Table 4.7 This content is available for free at http://textbookequit... |
awal rate from an elementary physics course is 30% for any given term. This implies that, for any given term, 70% of the students stay in the class for the entire term. A "success" could be defined as an individual who withdrew. The random variable X = the number of students who withdraw from the randomly selected elem... |
e the recorder. There are two trials. However, the trials are not independent because the outcome of the first trial affects the outcome of the second trial. The probability of a student on the first draw is 6 16 . The probability of a student on the second draw is 5 15 , when the first draw selects a student. The prob... |
s? The two groups are jelly beans and gumdrops. Since the probability question asks for the probability of picking gumdrops, the group of interest (first group) is gumdrops. The size of the group of interest (first group) is 80. The size of the second group is 100. The size of the sample is 50 (jelly beans or gumdrops)... |
about 0.1734: P(x > 1) = 1 − poissoncdf(0.75, 1). The graph of X ~ P(0.75) is: 250 CHAPTER 4 | DISCRETE RANDOM VARIABLES Figure 4.5 The y-axis contains the probability of x where X = the number of calls in 15 minutes. 4.29 A customer service center receives about ten emails every half-hour. What is the probability that... |
swers to four decimal places. 1. P(x = 3) = _________________ 2. P(0 < x < 3) = _________________ 3. P(x ≥ 2) = _________________ Use the data from the Organize the Data section to calculate the following answers. Round your answers to four decimal places. 1. RF(x = 3) = _________________ 2. RF(0 < x < 3) = ___________... |
distribution. The random variable X = the number of items from the group of interest. The distribution of X is denoted X ~ H(r, b, n), where r = the size of the group of interest (first group), b = the size of the second group, and n = the size of the chosen sample. It follows that n ≤ r + b. The mean of X is μ = nr r... |
es”? 44. What is the probability that at least two of the freshmen reply “yes”? 4.4 Geometric Distribution Use the following information to answer the next six exercises: The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and u... |
nts, eight classes have space for 60 students, one class has space for 70 students, and four classes have space for 100 students. a. What is the average class size assuming each class is filled to capacity? b. Space is available for 980 students. Suppose that each class is filled to capacity and select a statistics stu... |
for the player. f. Calculate the average expected earnings over the long run of playing this game for the player. g. Determine who has the advantage, the player or the house. 102. According to The World Bank, only 9% of the population of Uganda had access to electricity as of 2009. Suppose we randomly sample 150 peopl... |
he (i) mean and (ii) standard deviation of X. 4.6 Poisson Distribution SH.DYN.AIDS.ZS?order=wbapi_data_value_2011+wbapi_data_value+wbapi_data_value-last&sort=desc (accessed May 15, 2013). This content is available for free at http://textbookequity.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 C... |
ds.org/2010/02/24/millennials-confident-connected-open-tochange/ (accessed May 15, 2013). total “Prevalence of HIV, http://data.worldbank.org/indicator/ SH.DYN.AIDS.ZS?order=wbapi_data_value_2011+wbapi_data_value+wbapi_data_value-last&sort=desc (accessed May 15, 2013). (% of populations ages 15-49),” The World Bank, 20... |
~ G( 29 192 ) h. 0.3881 i. 6.6207 pages 109 0, 1, 2, and 3 111 a. X ~ G(0.25) b. i. Mean = μ = 1 p = 1 0.25 = 4 ii. Standard Deviation = σ = 1 − p p2 = 1 − 0.25 0.252 ≈ 3.4641 c. P(x = 10) = geometpdf(0.25, 10) = 0.0188 d. P(x = 20) = geometpdf(0.25, 20) = 0.0011 e. P(x ≤ 5) = geometcdf(0.25, 5) = 0.7627 113 a. X = the... |
quity.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 CHAPTER 5 | CONTINUOUS RANDOM VARIABLES 293 10.4 19.6 18.8 13.9 17.8 16.8 21.6 17.9 12.5 11.1 4.9 12.8 14.8 22.8 20.0 15.9 16.3 13.4 17.1 14.5 19.0 22.8 1.3 5.8 8.9 0.7 6.9 9.4 8.9 2.6 9.4 11.9 10.9 7.3 5.9 5.8 7.6 21.7 11.8 3.4 10.0 3.3 6.7 3... |
h percentile of repair times is 2.25 hours. 30% of repair times are 2.5 hours or less. Solution 5.6 d. Figure 5.21 Uniform Distribution between 1.5 and 4 with an area of 0.25 shaded to the right representing the longest 25% of repair times. P(x > k) = 0.25 P(x > k) = (base)(height) = (4 – k)(0.4) 0.25 = (4 – k)(0.4); S... |
e of 30 customers per hour arrive at a store and the time between arrivals is exponentially distributed. a. On average, how many minutes elapse between two successive arrivals? b. When the store first opens, how long on average does it take for three customers to arrive? c. After a customer arrives, find the probabilit... |
ta from a random number generator with the uniform distribution. Collect the Data Use a random number generator to generate 50 values between zero and one (inclusive). List them in Table 5.3. Round the numbers to four decimal places or set the calculator MODE to four places. 1. Complete the table. __________ __________... |
TER 5 | CONTINUOUS RANDOM VARIABLES 319 Figure 5.39 4. What does the shaded area represent? P(___< x < ___) Figure 5.40 5. What does the shaded area represent? P(___< x < ___) Figure 5.41 6. For a continuous probablity distribution, 0 ≤ x ≤ 15. What is P(x > 15)? 7. What is the area under f(x) if the function is a cont... |
σ = _______ g. Find the probability that the commuter waits less than one minute. h. Find the probability that the commuter waits between three and four minutes. i. Sixty percent of commuters wait more than how long for the train? State this in a probability question, similarly to parts g and h, draw the picture, and f... |
son elapses with a single no-hitter? b. If an entire season elapses without any no-hitters, what is the probability that there are no no-hitters in the following season? c. What is the probability that there are more than 3 no-hitters in a single season? 98. During the years 1998–2012, a total of 29 earthquakes of magn... |
nd P(X > 8) = 1 – P(X ≤ 8) ≈ 0.0311. This content is available for free at http://textbookequity.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 CHAPTER 6 | THE NORMAL DISTRIBUTION 337 6 | THE NORMAL DISTRIBUTION Figure 6.1 If you ask enough people about their shoe size, you will find that your g... |
, 1.27, right 6.3 Use the information in Example 6.3 to answer the following questions. a. Suppose a 15 to 18-year-old male from Chile was 176 cm tall from 2009 to 2010. The z-score when x = 176 cm is z = _______. This z-score tells you that x = 176 cm is ________ standard deviations to the ________ (right or left) of ... |
is used for entertainment between 1.8 and 2.75 hours per day. Solution 6.9 a. Let X = the amount of time (in hours) a household personal computer is used for entertainment. X ~ N(2, 0.5) where μ = 2 and σ = 0.5. Find P(1.8 < x < 2.75). The probability for which you are looking is the area between x = 1.8 and x = 2.75.... |
llected complete the following statements. (Hint: order the data) REMEMBER (IQR = Q3 – Q1) • IQR = _______ • The 15th percentile is _______. • The 85th percentile is _______. • Median is _______. • What is the theoretical probability that a randomly chosen pinky length is more than 6.5 cm? • Explain the meaning of the ... |
y.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 CHAPTER 6 | THE NORMAL DISTRIBUTION 359 Figure 6.17 b. P(__________ < x < __________) = __________ 59. Find the 70th percentile of the distribution for the time a CD player lasts. a. Sketch the situation. Label and scale the axes. Shade the region... |
__(_____,_____) c. If one of the trials is randomly chosen, find the probability that it lasted at least 24 days. Sketch the graph and write the probability statement. d. Sixty percent of all trials of this type are completed within how many days? 80. Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds pe... |
z-score formula. z = 1.5424. The height 85 inches is 1.5424 standard deviations above the mean. An NBA player whose height is 85 inches is taller than average. c. Height = 79 + 3.5(3.89) = 90.67 inches, which is over 7.7 feet tall. There are very few NBA players this tall so the answer is no, not likely. 65 a. iv b. K... |
tandard deviation of the original distribution sample size = n standard deviation sample size ⎞ ⎠ Example 7.1 An unknown distribution has a mean of 90 and a standard deviation of 15. Samples of size n = 25 are drawn randomly from the population. a. Find the probability that the sample mean is between 85 and 92. Solutio... |
rted Oct. 29, 2012 on the Flurry Blog, the mean age of tablet users is 34 years. Suppose the standard deviation is 15 years. The sample of size is 50. a. What are the mean and standard deviation for the sum of the ages of tablet users? What is the distribution? b. Find the probability that the sum of the ages is betwee... |
but change the sample size to 144. a. Find P(20 < x¯ < 30). b. Find P(Σx is at least 3,000). c. Find the 75th percentile for the sample mean excess time of 144 customers. d. Find the 85th percentile for the sum of 144 excess times used by customers. Example 7.10 In the United States, someone is sexually assaulted ever... |
Record the values of the change in Table 7.1. __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ __________ _________... |
en simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. Standard Error of the Mean the standard deviation of the distribu... |
atteries last. 53. Find the IQR for the mean amount of time 64 batteries last. 54. Find the middle 80% for the total amount of time 64 batteries last. Use the following information to answer the next eight exercises: A uniform distribution has a minimum of six and a maximum of ten. A sample of 50 is taken. 55. Find P(Σ... |
istribution of the averages. Start at x = -0.0005. Use bar widths of ten. h. Does this histogram look like the graph in part c? i. In one or two complete sentences, explain why the graphs either look the same or look different? j. Based upon the theory of the central limit theorem, X ¯ ~ _____(_____,____) Use the follo... |
he city. You plan to budget an average of 1.1 hours per technician to complete the work. Will this be enough time? 96. A typical adult has an average IQ score of 105 with a standard deviation of 20. If 20 randomly selected adults are given an IQ tesst, what is the probability that the sample mean scores will be between... |
standard deviation for the sample mean is σ n = 1 100 = 0.1 . The empirical rule, which applies to bell-shaped distributions, says that in approximately 95% of the samples, the sample mean, x¯ , will be within two standard deviations of the population mean μ. For our iTunes example, two standard deviations is (2)(0.1)... |
nterval estimate for the population mean exam score (the mean score on all exams). Find a 90% confidence interval for the true (population) mean of statistics exam scores. Solution 8.2 • You can use technology to calculate the confidence interval directly. • The first solution is shown step-by-step (Solution A). • The ... |
the same sample mean. Find a 90% confidence interval estimate for the population mean delivery time. Working Backwards to Find the Error Bound or Sample Mean When we calculate a confidence interval, we find the sample mean, calculate the error bound, and use them to calculate the confidence interval. However, sometimes... |
the confidence interval, you need the sample mean, x¯ , and the EBM. x¯ = 8.2267 s = 1.6722 n = 15 df = 15 – 1 = 14 CL so α = 1 – CL = 1 – 0.95 = 0.05 α 2 = 0.025 t α 2 = t0.025 The area to the right of t0.025 is 0.025, and the area to the left of t0.025 is 1 – 0.025 = 0.975 = t0.025 = 2.14 using invT(.975,14) on the T... |
.032 p ' – EBP = 0.842 – 0.032 = 0.81 p′ + EBP = 0.842 + 0.032 = 0.874 The confidence interval for the true binomial population proportion is (p′ – EBP, p′ + EBP) = (0.810, 0.874). Interpretation We estimate with 95% confidence that between 81% and 87.4% of all adult residents of this city have cell phones. Explanation... |
estimated (sample) proportion is within three percentage points of the true population proportion of all customers aged 50+ who use text messaging on their cell phones. 8.14 Suppose an internet marketing company wants to determine the current percentage of customers who click on ads on their smartphones. How many cust... |
s depends on: • • • the desired confidence level, information that is known about the distribution (for example, known standard deviation), the sample and its size. Confidence Level (CL) the percent expression for the probability that the confidence interval contains the true population parameter; for example, if the C... |
the degrees of freedom for a Student’s t- PRACTICE p′ is a point estimate for ρ s is a point estimate for σ 8.1 A Single Population Mean using the Normal Distribution 444 CHAPTER 8 | CONFIDENCE INTERVALS Use the following information to answer the next five exercises: The standard deviation of the weights of elephants ... |
ecisions. State the confidence interval, sketch the graph, and calculate the error bound. 68. List two difficulties the company might have in obtaining random results, if this survey were done by email. Use the following information to answer the next five exercises: Of 1,050 randomly selected adults, 360 identified 44... |
rror bound. c. Create a 95% confidence interval for the mean total individual contributions. d. Interpret the confidence interval in the context of the problem. 102. The American Community Survey (ACS), part of the United States Census Bureau, conducts a yearly census similar to the one taken every ten years, but with ... |
aken of size 14, what percent of the confidence intervals constructed should contain the population mean worth of coupons? Explain why. Use the following information to answer the next two exercises: A quality control specialist for a restaurant chain takes a random sample of size 12 to check the amount of soda served ... |
) conclude that at least half of all American adults believe this? 132. Public Policy Polling recently conducted a survey asking adults across the U.S. about music preferences. When asked, 80 of the 571 participants admitted that they have illegally downloaded music. a. Create a 99% confidence interval for the true pro... |
⎝0.8, (0.8)(0.2) 80 ⎞ ⎠ . (0.72171, 0.87829). 87 0.04 89 (0.72; 0.88) 91 With 92% confidence, we estimate the proportion of girls, ages 8 to 12, in a beginning ice-skating class at the Ice Chalet to be between 72% and 88%. 93 The error bound would increase. Assuming all other variables are kept constant, as the confide... |
samples taken from the population. Confidence intervals are one way to estimate a population parameter. Another way to make a statistical inference is to 470 CHAPTER 9 | HYPOTHESIS TESTING WITH ONE SAMPLE make a decision about a parameter. For instance, a car dealer advertises that its new small truck gets 35 miles pe... |
s a Boy Genetic Labs does not influence the gender outcome of a pregnancy when, in fact, it does. The probability of this error occurring is denoted by the Greek letter beta, β. The error of greater consequence would be the Type I error since couples would use the It’s a Boy Genetic Labs product in hopes of increasing ... |
ht is at most 15 cm.). There is sufficient evidence that the true mean height for the population of the baker's loaves of bread is greater than 15 cm. 9.9 A normal distribution has a standard deviation of 1. We want to verify a claim that the mean is greater than 12. A sample of 36 is taken with a sample mean of 12.5. ... |
se.) 9.14 The mean throwing distance of a football for a Marco, a high school freshman quarterback, is 40 yards, with a standard deviation of two yards. The team coach tells Marco to adjust his grip to get more distance. The coach records the distances for 20 throws. For the 20 throws, Marco’s mean distance was 45 yard... |
ercentages. Use the distribution for P′, the estimated proportion. P′ ~ N⎛ ⎝p, p ⋅ q n ⎞ ⎠ Therefore, P′ ~ N⎛ ⎝0.5, 0.5 ⋅ 0.5 100 ⎞ ⎠ where p = 0.50, q = 1−p = 0.50, and n = 100 Calculate the p-value using the normal distribution for proportions: p-value = P (p′ < 0.47 or p′ > 0.53) = 0.5485 where x = 53, p′ = x n = 53... |
eater than one. Example 9.21 In a study of 420,019 cell phone users, 172 of the subjects developed brain cancer. Test the claim that cell phone users developed brain cancer at a greater rate than that for non-cell phone users (the rate of brain cancer for non-cell phone users is 0.0340%). Since this is a critical issue... |
theses In a hypothesis test, sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: 1. Evaluate the null hypothesis, typically denoted with H0. The null is not r... |
st is testing a water sample for E-coli. Suppose the null hypothesis, H0, is: the sample does not contain E-coli. The probability that the sample does not contain E-coli, but the microbiologist thinks it does is 0.012. The probability that the sample does contain E-coli, but the microbiologist thinks it does not is 0.0... |
age, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test. The null and alternative hypotheses are: a. Ho:... |
othesis test to see if your decision and conclusion would change if your belief were that the brown trout’s mean I.Q. is not four. 506 CHAPTER 9 | HYPOTHESIS TESTING WITH ONE SAMPLE 83. According to an article in Newsweek, the natural ratio of girls to boys is 100:105. In China, the birth ratio is 100: 114 (46.7% girls... |
purpose thou thyself sent me forth, I did discover that one-and-forty believe fervently that the spirits of the dead walk with us. Before my God, I might not this believe, without the sensible and true avouch of mine own eyes. POLONIUS: Give thine own thoughts no tongue, Horatio. (Polonius turns to Hamlet.) But look to... |
percent of EVC students who attended the midnight showing of Harry Potter is at least 20%. 106. Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours... |
his is a two-tailed test. 53 516 CHAPTER 9 | HYPOTHESIS TESTING WITH ONE SAMPLE Figure 9.25 55 a right-tailed test 57 a left-tailed test 59 This is a left-tailed test. 61 This is a two-tailed test. 62 a. H0: μ = 34; Ha: μ ≠ 34 b. H0: p ≤ 0.60; Ha: p > 0.60 c. H0: μ ≥ 100,000; Ha: μ < 100,000 d. H0: p = 0.29; Ha: p ≠ 0.... |
o support the claim that less than 50% of his friends have pierced ears. i. Confidence Interval: (0.245, 0.515): The “plus-4s” confidence interval is (0.259, 0.519). 98 a. H0: p = 0.40 b. Ha: p < 0.40 c. Let P′ = the proportion of schoolmates who fear public speaking. d. normal for a single proportion e. –1.01 f. p-val... |
believed to be the same. A study is done and data are collected, resulting in the data in Table 10.1. Each populations has a normal distribution. Sample Size Average Number of Hours Playing Sports Per Day Sample Standard Deviation Girls 9 Boys 16 Table 10.1 2 3.2 0.866 1.00 Is there a difference in the mean amount of t... |
m or large? Explain what the size of the effect means for this problem. Solution 10.5 d = 0.834; Large, because 0.834 is greater than Cohen’s 0.8 for a large effect size. The size of the differences between the means of the Final Exam scores of online students and students in a face-to-face class is large indicating a ... |
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