Chapter 10Reveiw
Researchers are studying the distribution of subscribers to a certain streaming service in different populations. From a random sample of 200 people in City C, 34 were found to subscribe to the streaming service. From a random sample of 200 people in City K, 54 were found to subscribe to the streaming service. Assuming all conditions for inference are met, which of the following is a 90 percent confidence interval for the difference in population proportions (City C minus City K) who subscribe to the streaming service?
Correct :0.17−0.27)±1.65(0.17)(0.83)+(0.27)(0.73)200−−−−−−−−−−−−−−−√ My Awnser: 0.17−0.27)±1.65(0.17)(0.83)+(0.27)(0.73)200−−−−−−−−−−−−−−−√
A fitness center piloted two new programs to help people reduce stress levels and maintain a healthy lifestyle. After one month, 112 of the 125 people who volunteered for a program in mindfulness reported a reduction in stress levels, and 110 of the 135 people who volunteered for a yoga program reported a reduction in stress levels. The fitness center wants to investigate whether there is a significant difference between the proportions of all people in the two programs who would report reductions in stress levels. Have the conditions for inference been met?
Correct Awnser:A No, because the samples were not selected or assigned using a random method My Awnser:No, because the normality of the sampling distribution cannot be assumed; the number of people who did not experience stress relief is not large enough
Maria has two routes, E and W, she can take when commuting to work. Both routes go through a railroad crossing, and sometimes she needs to stop at the crossing to allow trains to pass. She claims that the proportion of times she needs to stop when taking route E is different from the proportion of times she needs to stop when taking route W. She conducted the following hypothesis test at the significance level of α=0.10. H0:pE=pWHa:pE≠pW In the hypotheses, pE represents the proportion of times she needs to stop at the crossing when using route E, and pW represents the proportion of times she needs to stop at the crossing when using route W. All conditions for inference were met, and the resulting p-value was 0.37. Which of the following is the correct decision for the test?
Correct Awnser:B The pp-value is greater than αα, and the null hypothesis is not rejected. There is convincing evidence to support the claim that the proportion of times she needs to stop at the crossing is the same for the different routesMy Awnser:B The pp-value is greater than αα, and the null hypothesis is not rejected. There is convincing evidence to support the claim that the proportion of times she needs to stop at the crossing is the same for the different routes
A sociologist will conduct a two-sample t-test for a difference in means to investigate whether there is a significant difference, on average, between the salaries of people with bachelor's degrees and people with master's degrees. From a random sample of 32 people with a bachelor's degree, the average salary was $55,000 with standard deviation $3,500. From a random sample of 28 people with a master's degree, the average salary was $58,000 with a standard deviation of $4,000. With a null hypothesis of no difference in the means, which of the following is the test statistic for the appropriate test to investigate whether there is a difference in population means (master's degree minus bachelor's degree) ?
Correct Awnser:B t=(58,000−55,000)4,000228+3,500232√ My Awnser:C t=(58,000−55,000)4,000228+3,500232−−−−−−−−−−√
A sociologist will conduct a two-sample t-test for a difference in means to investigate whether there is a significant difference, on average, between the salaries of people with bachelor's degrees and people with master's degrees. From a random sample of 32 people with a bachelor's degree, the average salary was $55,000 with standard deviation $3,500. From a random sample of 28 people with a master's degree, the average salary was $58,000 with a standard deviation of $4,000. With a null hypothesis of no difference in the means, which of the following is the test statistic for the appropriate test to investigate whether there is a difference in population means (master's degree minus bachelor's degree) ?
Correct Awnser:B t=(58,000−55,000)4,000228+3,500232√ My Awnser:C t=(58,000−55,000)4,000228+3,500232−−−−−−−−−−√t=(58,000−55,000)4,000228+3,500232
A soda manufacturer claims that its Cherry Fizz soda has more carbonation than a competitor's Cherry Eclipse soda. Bottles of both types of soda are opened, covered with a balloon, and then shaken. The diameter of each balloon is then measured. The mean balloon diameters are 2.3 inches for the Cherry Fizz soda and 2.1 inches for the Cherry Eclipse soda. A 90 percent confidence interval to estimate the difference in mean diameters, in inches, is (−0.8,1.2). Which of the following claims is supported by the interval?
Correct Awnser:Because the interval contains 0, it is possible that there is no difference in mean carbonation levels. My Awnser:Because the interval contains 0, it is possible that there is no difference in mean carbonation levels.
Two siblings, Alice and Sean, are both convinced that they are faster than the other at solving a puzzle cube. They recorded the length of time it took them to solve the cube 18 times each during a one-month period. Then each calculated the mean amount of time and standard deviation, in minutes, for their times. Let μA equal the mean time it took Alice to solve the puzzle cube and μS equal the mean time it took Sean. Which of the following are the appropriate null and alternative hypotheses to test for a difference in time for the siblings to solve the cube?
Correct Awnser:C H0:μA−μS=0Ha:μA−μS≠0My Awnser:A H0:μA−μS=0Ha:μA−μS>0
Animal researchers studying cows and horses conducted a two-sample t-test for a difference in means to investigate whether grazing cows eat more grass, on average, than grazing horses. All conditions for inference were met, and the test produced a test statistic of t=1.664 and a p-value of 0.0487. Which of the following is a correct interpretation of the p-value?
Correct Awnser:E Assuming that the mean amount of grass eaten by cows is equal to the mean amount of grass eaten by horses, the probability of observing a test statistic of at least 1.664 is 0.0487. My Awnser:D Assuming that the mean amount of grass eaten by cows is equal to the mean amount of grass eaten by horses, the probability of observing a test statistic of at most 1.664 is 0.0487.
Market researchers interviewed a random sample of 60 men and a random sample of 55 women about their preferences for different color designs for the packaging of a certain product. Of those interviewed, 23 men and 28 women preferred color design X. Which of the following is the correct test statistic for a two-sample z-test for a difference in population proportions for men and women (men minus women) in their preference for color design X ?
Correct Awnser:E z=0.38−0.51(0.44)(0.56)(160+155)√ My Awnser:=0.38−0.51(0.44)(0.56)(160+55)√
Because library books are read many times, glue is often applied to the spine of a book to keep the pages tight. A glue is considered successful if a book lasts at least 6 months before needing to be reglued. Two brands of glue, G and K, were tested to determine whether there was a difference in the proportion of books lasting at least 6 months. Let pG represent the proportion of books lasting at least 6 months when glued with G, and let pK represent the proportion of books lasting at least 6 months when glued with K. The following hypothesis test was conducted at the significance level of α=0.01. H0:pG=pKHa:pG≠pK All conditions for inference were met, and the resulting p-value was 0.006. Which of the following is the correct decision for the test?
Correct Awnser:The pp-value is less than αα, and the null hypothesis is rejected. There is convincing evidence to support the claim that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K. My Awnser:The pp-value is less than αα, and the null hypothesis is rejected. There is not convincing evidence to support the claim that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K.
A 95 percent confidence interval for the proportion difference p1−p2 was calculated to be (−0.12,0.17). Which of the following conclusions is supported by the interval?
Correct Awnser:There is not sufficient evidence to determine which proportion is greater. My Awnser:There is evidence to conclude that p1>p2p1>p2 because the range of positive values in the interval is greater than the range of negative values.
Independent random samples of voters from two voting districts, G and H, were selected to investigate the proportion of all voters who favor a proposal to widen a road that runs through both districts. The difference between the sample proportions (G minus H) was used to create the 95 percent confidence interval (0.13,0.47) for the population difference between districts. Which of the following is the best interpretation of the interval?
Correct: C It is likely that more voters in district G favor the proposal than in district H, because all values in the interval are positive. My Awnser:t is likely that there is no difference between the districts in voters who favor the proposal, because 0 is not contained in the interval.
Health programs routinely study the number of days that patients stay in hospitals. In one study, a random sample of 12 men had a mean of 7.95 days and a standard deviation of 6.2 days, and a random sample of 19 women had a mean of 7.1 days and a standard deviation of 5.0 days. The sample data will be used to construct a 95 percent confidence interval to estimate the difference between men and women in the mean number of days for the length of stay at a hospital. Have the conditions been met for inference with a confidence interval?
Correct: No. The sample sizes are not large enough to assume that the sampling distribution of the difference in sample means is approximately normal. my Awnser: C No. The size of at least one of the samples is greater than 10 percent of the population.
A gardener wants to know if soaking seeds in water before planting them increases the proportion of seeds that germinate. To investigate, the gardener will assign 50 seeds to be soaked before planting and 50 seeds to be planted without being soaked. After two weeks, the gardener will record how many seeds in each group germinated and construct a 95 percent confidence interval for the difference in proportions. Which of the following conditions for inference should be met? The seeds should be randomly assigned to a treatment. The group sizes should be less than 10 percent of the population sizes. The number of successful seeds and unsuccessful seeds in each group should be at least 10.
Corrected Awnser: D I and III Only My Awnser: I and II Only
Which of the following is not a condition for constructing a confidence interval to estimate the difference between two population proportions?
Corrected Awsner:B The data must come from populations with approximately normal distributions My Answer:C When samples are taken without replacement, each population must be at least 10 times as large as its corresponding sample.
The weekly sales at two movie theaters were recorded for a random sample of 25 weeks. A 95 percent confidence interval for the difference in mean weekly sales for the two movie theaters was calculated as ($1,288,$2,586). With all else remaining constant, which of the following would have resulted in a confidence interval narrower than the calculated interval?
My Awnser:A sample size greater than 25 Correct Awnser:A sample size greater than 25
Consider a 95 percent confidence interval constructed for the difference between two population proportions pR and pS. The interval for pR−pS is given as (−0.05,0.15). Which of the following is an appropriate interpretation of the confidence level?
My Awnser:E In repeated random sampling with the same sample size, approximately 95 percent of the intervals will capture the difference in population proportions, pR−pSpR−pS. Correct:E In repeated random sampling with the same sample size, approximately 95 percent of the intervals will capture the difference in population proportions, pR−pSpR−pS.
The police in a certain city are investigating whether the proportion of minor traffic accidents is greater on Friday nights than on Sunday nights. As part of the investigation, they select a random sample of police calls from Friday nights and a random sample of police calls from Sunday nights. From both samples, they record the sample proportion of calls that involved minor traffic accidents. Let pF represent the proportion of all Friday night calls, and let pS represent the proportion of all Sunday night calls. Which of the following are the correct hypotheses for the investigation?
My awnser:D H0:pF=pSHa:pF>pS Correct Awnser: D H0:pF=pSHa:pF>pS
There are 1,000 golden delicious and 1,000 red delicious apples in a cooler. In a random sample of 75 of the golden delicious apples, 48 had blemishes. In a random sample of 75 of the red delicious apples, 42 had blemishes. Assume all conditions for inference have been met. Which of the following is closest to the interval estimate of the difference in the numbers of apples with blemishes (golden delicious minus red delicious) at a 98 percent level of confidence?
correct awnser:(-105,265) my awnser:(-0.105,0.265)
A national consumer agency selected independent random samples of 45 owners of newer cars (less than five years old) and 40 owners of older cars (more than five years old) to estimate the difference in mean dollar cost of yearly routine maintenance, such as oil changes, tire rotations, filters, and wiper blades. The agency found the mean dollar cost per year for newer cars was $195 with a standard deviation of $46. For older cars, the mean was $286 with a standard deviation of $58. Which of the following represents the 95 percent confidence interval to estimate the difference (newer minus older) in the mean dollar cost of routine maintenance between newer and older cars?
correct:(195−286)±1.99246245+58240−−−−−−−−√(195−286)±1.99246245+58240 My Awnser:(195−286)±1.992462+58245+40−−−−−−√
