Hypothesis testing-Practice questions, Exercises of Statistics

Download Hypothesis testing-Practice questions and more Exercises Statistics in PDF only on Docsity! Chapter 09 1. The null hypothesis typically corresponds to a presumed default state of nature. True False 2. The alternative hypothesis typically agrees with the status quo. True False 3. On the basis of sample information, we either "accept the null hypothesis" or "reject the null hypothesis." True False 4. As a general guideline, we use the alternative hypothesis as a vehicle to establish something new, or contest the status quo, for which a corrective action may be required. True False 5. In a one-tailed test, the rejection region is located under one tail (left or right) of the corresponding probability distribution, while in a two-tailed test this region is located under both tails. True False 6. A Type I error is committed when we reject the null hypothesis, which is actually true. True False 7. A Type II error is made when we reject the null hypothesis and the null hypothesis is actually false. True False 8. For a given sample size, any attempt to reduce the likelihood of making one type of error (Type I or Type II) will increase the likelihood of the other error. True False 9. A hypothesis test regarding the population mean µ is based on the sampling distribution of the sample mean True False 10. Under the assumption that the null hypothesis is true as an equality, the p-value is the likelihood of observing a sample mean that is at least as extreme as the one derived from the given sample. True False 11. The critical value approach specifies a range of values, also called the rejection region, such that if the value of the test statistic falls into this range, we do not reject the null hypothesis. True False 12. The hypothesis statement H: µ = 25 is an example of a(an) ________ hypothesis. _________________________ 13. The hypothesis statement H: < 60 is an example of a(an) ________ hypothesis. _________________________ 14. A(n) ______ error is committed when we reject the null hypothesis when the null hypothesis is true. _________________________ 15. We define the allowed probability of making a Type I error as α, and we refer to 100α % as the ____________. _________________________ 16. If we reject a null hypothesis at the 1% significance level, then we have _________ evidence that the null hypothesis is false. _________________________ 26. The national average for an eighth-grade reading comprehension test is 73. A school district claims that its eighth-graders outperform the national average. In testing the school district’s claim, how does one define the population parameter of interest? A. The mean score on the eighth-grade reading comprehension test B. The number of eighth graders who took the reading comprehension test C. The standard deviation of the score on the eighth-grade reading comprehension test D. The proportion of eighth graders who scored above 73 on the reading comprehension test 27. A local courier service advertises that its average delivery time is less than 6 hours for local deliveries. When testing the two hypotheses, Ho:μ ≥ 6 and HA:μ < 6, μ stand for _____________. A. the mean delivery time B. the standard deviation of the delivery time C. the number of deliveries that took less than 6 hours D. the proportion of deliveries that took less than 6 hours 28. It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. In testing the politician’s claim, how does one define the population parameter of interest? A. The current proportion of babies born out of wedlock B. The mean number of babies born out of wedlock C. The number of babies born out of wedlock D. The general belief that the proportion of babies born out of wedlock is no more than 0.50 29. It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. When testing the two hypotheses, H0: p ≤ 0.50 and HA: p > 0.50, p stands for _____________. A. the current proportion of babies born out of wedlock B. the mean number of babies born out of wedlock C. the number of babies born out of wedlock D. the general belief that the proportion of babies born out of wedlock is no more than 0.50 30. It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. Identify the correct null and alternative hypotheses to test the politician’s claim. A. H0:p = 0.50 and HA:p ≠ 0.50 B. H0:p ≤ 0.50 and HA:p > 0.50 C. H0:p ≥ 0.50 and HA:p > 0.50 D. H0:p ≥ 0.50 and HA:p < 0.50 31. Many cities around the United States are installing LED streetlights, in part to combat crime by improving visibility after dusk. An urban police department claims that the proportion of crimes committed after dusk will fall below the current level of 0.84 if LED streetlights are installed. Specify the null and alternative hypotheses to test the police department’s claim. A. H0:p = 0.84 and HA:p ≠ 0.84 B. H0:p < 0.84 and HA:p ≥ 0.84 C. H0:p ≤ 0.84 and HA:p > 0.84 D. H0:p ≥ 0.84 and HA:p < 0.84 32. A professional sports organization is going to implement a test for steroids. The test gives a positive reaction in 94% of the people who have taken the steroid. However, it erroneously gives a positive reaction in 4% of the people who have not taken the steroid. What is the probability of Type I and Type II errors giving the null hypothesis "the individual has not taken steroids." A. Type I: 4%, Type II: 6% B. Type I: 6%, Type II: 4% C. Type I: 94%, Type II: 4% D. Type I: 4%, Type II: 94% 38. Consider the following hypotheses that relate to the medical field: Ho: A person is free of disease. HA: A person has disease. In this instance, a Type I error is often referred to as ___________. A. a false positive B. a false negative C. a negative result D. the power of the test 39. Consider the following hypotheses that relate to the medical field: Ho: A person is free of disease. HA: A person has disease. In this instance, a Type II error is often referred to as ___________. A. a false positive B. a false negative C. a negative result D. the power of the test 40. A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: Ho: μ ≤ 300. HA: μ > 300. The consequences of committing a Type I error would be that____________________________. A. the franchiser builds on an acceptable site B. the franchiser builds on an unacceptable site C. the franchiser does not build on an acceptable site D. the franchiser does not build on an unacceptable site 41. A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: Ho: μ ≤ 300. HA: μ > 300. The consequences of committing a Type II error would be that__________________________. A. the franchiser builds on an acceptable site B. the franchiser builds on an unacceptable site C. the franchiser does not build on an acceptable site D. the franchiser does not build on an unacceptable site 42. A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. If the advisor tests the hypotheses Ho: μ ≤ 300 versus HA: μ > 300, μ stands for ____________. A. the average number of automobiles that pass the intersection per hour B. the number of automobiles that pass the intersection per hour C. the proportion of automobiles that pass the intersection per hour D. the standard deviation of the number of automobiles that pass the intersection per hour 48. When conducting a hypothesis test concerning the population proportion, the value of the test statistic is calculated as ____________. A. B. C. D. 49. Which of the following represents an appropriate set of hypotheses? A. B. C. D. 50. If the chosen significance level is α = 0.05, then ____________________________________________. A. there is a 5% probability of rejecting a true null hypothesis B. there is a 5% probability of accepting a true null hypothesis C. there is a 5% probability of rejecting a false null hypothesis D. there is a 5% probability of accepting a false null hypothesis 51. When conducting a hypothesis test for a given sample size, if a is increased from 0.05 to 0.10, then __________________. A. the probability of incorrectly rejecting the null hypothesis increases B. the probability of incorrectly failing to reject the null hypothesis decreases C. the probability of Type II error decreases D. All of the above 52. When conducting a hypothesis test for a given sample size, if the probability of a Type I error decreases, then the ______________________________________. A. probability of Type II error decreases B. probability of incorrectly rejecting the null hypothesis increases C. probability of incorrectly accepting the null hypothesis increases D. probability of incorrectly accepting the null hypothesis decreases 53. Which of the following are one-tailed tests? A. Ho:μ ≤ 10, HA:μ > 10 B. Ho:μ = 10, HA:μ ≠ 10 C. Ho:μ ≥ 400, HA:μ < 400 D. Both Ho:μ ≤ 10, HA:μ > 10 and Ho:μ ≥ 400, HA:μ < 400 54. Which of the following are two-tailed tests? A. Ho:μ ≤ 10, HA:μ > 10 B. Ho:μ = 10, HA:μ ≠ 10 C. Ho:μ ≥ 400, HA:μ < 400 D. Both Ho:μ ≤ 10, HA:μ > 10 and Ho:μ ≥ 400, HA:μ < 400 60. A one-tailed hypothesis test of the population mean has ______________. A. only one critical value B. two critical values, both positive C. two critical values, both negative D. two critical values, one positive and one negative 61. Consider the following competing hypotheses: Ho:μ = 0, HA:μ ≠ 0. The value of the test statistic is z = −1.38. If we choose a 5% significance level, then we ___________________________________________. A. reject the null hypothesis and conclude that the population mean is significantly different from zero B. reject the null hypothesis and conclude that the population mean is not significantly different from zero C. do not reject the null hypothesis and conclude that the population mean is significantly different from zero D. do not reject the null hypothesis and conclude that the population mean is not significantly different from zero 62. A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. The parameter to be tested is ___________________________. A. the mean GPA of all university students B. the mean GPA of the university honors students C. the mean GPA of 3.60 for the 36 selected honors students D. the proportion of honors students with a GPA exceeding 3.50 63. A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. To establish whether the mean GPA exceeds 3.50, the appropriate hypotheses are ______________. A. B. C. D. 64. A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. The value of the test statistic is ____________. A. z = – 1.50 B. t35 = – 1.50 C. z = 1.50 D. t35 = 1.50 65. A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. At a 5% significance level, the critical value(s) is(are) ________. A. 1.64 5 B. 1.69 0 C. –1.96 and 1.96 D. –2.030 and 2.030 66. A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. At a 5% significance level, the decision is to _____________. A. reject Ho we can conclude that the mean GPA is significantly greater than 3.50 B. reject Ho we cannot conclude that the mean GPA is significantly greater than 3.50 C. not reject Ho we can conclude that the mean GPA is significantly greater than 3.50 D. not reject Ho we cannot conclude that the mean GPA is significantly greater than 3.50 70. The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350. At a 5% significance level, the critical value(s) is(are) ___________. A. 1.64 5 B. – 1.645 C. –1.96 and 1.96 D. –2.030 and 2.030 71. The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350. At the 5% significance level, the decision is to ___________. A. reject Ho; we can conclude that the mean number of customers visiting the dealership is significantly less than 800 B. reject Ho; we cannot conclude that the mean number of customers visiting the dealership is significantly less than 800 C. do not reject Ho; we can conclude that the mean number of customers visiting the dealership is significantly less than 800 D. do not reject Ho;we cannot conclude that the mean number of customers visiting the dealership is significantly less than 800 72. The Boston public school district has had difficulty maintaining on-time bus service for its students ("A Year Later, School Buses Still Late," Boston Globe, October 5, 2011). Suppose the district develops a new bus schedule to help combat chronic lateness on a particularly woeful route. Historically, the bus service on the route has been, on average, 12 minutes late. After the schedule adjustment, the first 36 runs were an average of eight minutes late. As a result, the Boston public school district claimed that the schedule adjustment was an improvement—students were not as late. Assume a population standard deviation for bus arrival time of 12 minutes. Which of the following can be used to determine whether the schedule adjustment reduced the average lateness time of 12 minutes? A. B. C. D. 75. The Boston public school district has had difficulty maintaining on-time bus service for its students ("A Year Later, School Buses Still Late," Boston Globe, October 5, 2011). Suppose the district develops a new bus schedule to help combat chronic lateness on a particularly woeful route. Historically, the bus service on the route has been, on average, 12 minutes late. After the schedule adjustment, the first 36 runs were an average of eight minutes late. As a result, the Boston public school district claimed that the schedule adjustment was an improvement—students were not as late. Assume a population standard deviation for bus arrival time of 12 minutes. At the 1% significance level, does the evidence support the Boston public schools’ claim? A. No, because the p-value is greater than α. B. Yes, because thep-value is greater than α. C. No, because the value of the test statistic is less than the critical value. D. Yes, because the value of the test statistic is less than the critical value. 76. An analyst conducts a hypothesis test to check whether the mean return for a particular fund differs from 10%. He assumes that returns are normally distributed and sets up the following competing hypotheses: Ho:μ = 10,HA:μ ≠ 10 Over the past 10 years the fund has had an average annual return of 13.4% with a standard deviation of 2.6%. The value of the test statistic is 4.14 and the critical values at the 5% significance level are−2.262 and 2.262.The correct decision is to ____________________________________. A. reject Ho; we can conclude that the mean differs from 10% B. reject Ho; we cannot conclude that the mean differs from 10% C. not reject Ho; we can conclude that the mean differs from 10% D. not reject Ho; we cannot conclude that the mean differs from 10% 77. A 99% confidence interval for the population mean yields the following results: [−3.79, 5.86].At the 1% significance level, what decision should be made regarding the following hypothesis test with Ho:μ = 0,HA:μ ≠ 0? A. Reject Ho; we can conclude that the mean differs from zero. B. Reject Ho; we cannot conclude that the mean differs from zero. C. Do not reject Ho; we can conclude that the mean differs from zero. D. Do not reject Ho; we cannot conclude that the mean differs from zero. 78. To test if the mean IQ of employees in an organization is greater than 100, a sample of 30 employees is taken and the value of the test statistic is computed as t29 = 2.42 If we choose a 5% significance level, we _____________. A. reject the null hypothesis and conclude that the mean IQ is greater than 100 B. reject the null hypothesis and conclude that the mean IQ is not greater than 100 C. do not reject the null hypothesis and conclude that the mean IQ is greater than 100 D. do not reject the null hypothesis and conclude that the mean IQ is not greater than 100 83. A schoolteacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L. The school samples the air for 36 days and finds an average concentration of 4.4pCi/L with a standard deviation of 1pCi/L. At a 5% significance level, the critical value(s) is(are) _______. A. −1.69 0 B. 1.69 0 C. −1.96 and 1.96 D. −2.030 and 2.030 84. A schoolteacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L. The school samples the air for 36 days and finds an average concentration of 4.4pCi/L with a standard deviation of 1pCi/L. At a 5% significance level, the decision is to ________________________________________________. A. reject Ho; we can conclude that the mean concentration of radon gas is greater than the safe level B. reject Ho; we cannot conclude that the mean concentration of radon gas is greater than the safe level C. not reject Ho; we can conclude that the mean concentration of radon gas is greater than the safe level D. not reject Ho; we cannot conclude that the mean concentration of radon gas is greater than the safe level 85. A car dealer who sells only late-model luxury cars recently hired a new salesperson and believes that this salesperson is selling at lower markups. He knows that the long-run average markup in his lot is $5,600. He takes a random sample of 16 of the new salesperson’s sales and finds an average markup of $5,000 and a standard deviation of $800. Assume the markups are normally distributed. What is the value of an appropriate test statistic for the car dealer to use to test his claim? A. t15 = – 3.00 B. z = – 3.00 C. t15 = – 0.75 D. z = – 0.75 86. A manager at a temp agency believes that one of the agency’s recruiters has unorthodox methods and claims that the wages the recruiter secures for its temps differ from the agency’s average wage of $12 per hour. The agency takes a random sample of 49 recent contracts the recruiter secured and finds an average wage of $11.25 per hour and a standard deviation of $2.25 per hour. Does the evidence support the agency’s claim at the 5% significance level? A. Yes, because the p-value is greater than α, the claim is supported. B. No, because the p-value is not greater than α, the claim is not supported. C. Yes, because the value of the test statistic is less than the critical value, the claim is supported. D. No, because the value of the test statistic is greater than the critical value, the claim is not supported. 87. A newly hired basketball coach promised a high-paced attack that will put more points on the board than the team’s previously tepid offense historically managed. After a few months, the team owner looks at the data to test the coach’s claim. He takes a sample of 36 of the team’s games under the new coach and finds that they scored an average of 101 points with a standard deviation of 6 points. Over the past 10 years, the team had averaged 99 points. What is(are) the appropriate critical value(s) to test the new coach’s claim at the 1% significance level? A. −2.43 8 B. −2.438 and 2.438 C. 2.32 6 D. 2.43 8 88. A newly hired basketball coach promised a high-paced attack that will put more points on the board than the team’s previously tepid offense historically managed. After a few months, the team owner looks at the data to test the coach’s claim. He takes a sample of 36 of the team’s games under the new coach and finds that they scored an average of 101 points with a standard deviation of 6 points. Over the past 10 years, the team had averaged 99 points. What is the value of the appropriate test statistic to test the new coach’s claim at the 1% significance level? A. t35 = 0.33 B. z = 0.33 C. t35 = 2.00 D. z = 2.00 93. A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 200 graduates, 30 students have a GPA of 3.00 or below. The value of the test statistic and its associated p-value are ________________________. A. t199 = –1.77 and p-value = 0.0384 B. z = –1.77 and p-value = 0.0384 C. t199 = –1.77 and p-value = 0.0768 D. z = –1.77 and p-value = 0.0768 94. A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 200 graduates, 30 students have a GPA of 3.00 or below. At a 5% significance level, the decision is to _________________________________________________________________________.. A. reject Ho; we can conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20 B. reject Ho; we cannot conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20 C. not reject Ho; we can conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20 D. not reject Ho; we cannot conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20 95. The Institute of Education Sciences measures the high school dropout rate as the percentage of 16-through 24-year-olds who are not enrolled in school and have not earned a high school credential. In 2009, the high school dropout rate was 8.1%. A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. When testing whether the dropout rate has decreased, the appropriate hypotheses are _____________. A. B. C. D. Chapter 09 1. The null hypothesis typically corresponds to a presumed default state of nature. True False 2. The alternative hypothesis typically agrees with the status quo. True False 3. On the basis of sample information, we either "accept the null hypothesis" or "reject the null hypothesis." True False 4. As a general guideline, we use the alternative hypothesis as a vehicle to establish something new, or contest the status quo, for which a corrective action may be required. True False 5. In a one-tailed test, the rejection region is located under one tail (left or right) of the corresponding probability distribution, while in a two-tailed test this region is located under both tails. True False 6. A Type I error is committed when we reject the null hypothesis, which is actually true. True False 7. A Type II error is made when we reject the null hypothesis and the null hypothesis is actually false. True False 8. For a given sample size, any attempt to reduce the likelihood of making one type of error (Type I or Type II) will increase the likelihood of the other error. True False 9. A hypothesis test regarding the population mean µ is based on the sampling distribution of the sample mean True False 10. Under the assumption that the null hypothesis is true as an equality, the p-value is the likelihood of observing a sample mean that is at least as extreme as the one derived from the given sample. True False 11. The critical value approach specifies a range of values, also called the rejection region, such that if the value of the test statistic falls into this range, we do not reject the null hypothesis. True False 12. The hypothesis statement H: µ = 25 is an example of a(an) ________ hypothesis. _________________________ 13. The hypothesis statement H: < 60 is an example of a(an) ________ hypothesis. _________________________ 14. A(n) ______ error is committed when we reject the null hypothesis when the null hypothesis is true. _________________________ 15. We define the allowed probability of making a Type I error as α, and we refer to 100α % as the ____________. _________________________ 16. If we reject a null hypothesis at the 1% significance level, then we have _________ evidence that the null hypothesis is false. _________________________ 26. The national average for an eighth-grade reading comprehension test is 73. A school district claims that its eighth-graders outperform the national average. In testing the school district’s claim, how does one define the population parameter of interest? A. The mean score on the eighth-grade reading comprehension test B. The number of eighth graders who took the reading comprehension test C. The standard deviation of the score on the eighth-grade reading comprehension test D. The proportion of eighth graders who scored above 73 on the reading comprehension test 27. A local courier service advertises that its average delivery time is less than 6 hours for local deliveries. When testing the two hypotheses, Ho:μ ≥ 6 and HA:μ < 6, μ stand for _____________. A. the mean delivery time B. the standard deviation of the delivery time C. the number of deliveries that took less than 6 hours D. the proportion of deliveries that took less than 6 hours 28. It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. In testing the politician’s claim, how does one define the population parameter of interest? A. The current proportion of babies born out of wedlock B. The mean number of babies born out of wedlock C. The number of babies born out of wedlock D. The general belief that the proportion of babies born out of wedlock is no more than 0.50 29. It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. When testing the two hypotheses, H0: p ≤ 0.50 and HA: p > 0.50, p stands for _____________. A. the current proportion of babies born out of wedlock B. the mean number of babies born out of wedlock C. the number of babies born out of wedlock D. the general belief that the proportion of babies born out of wedlock is no more than 0.50 30. It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. Identify the correct null and alternative hypotheses to test the politician’s claim. A. H0:p = 0.50 and HA:p ≠ 0.50 B. H0:p ≤ 0.50 and HA:p > 0.50 C. H0:p ≥ 0.50 and HA:p > 0.50 D. H0:p ≥ 0.50 and HA:p < 0.50 31. Many cities around the United States are installing LED streetlights, in part to combat crime by improving visibility after dusk. An urban police department claims that the proportion of crimes committed after dusk will fall below the current level of 0.84 if LED streetlights are installed. Specify the null and alternative hypotheses to test the police department’s claim. A. H0:p = 0.84 and HA:p ≠ 0.84 B. H0:p < 0.84 and HA:p ≥ 0.84 C. H0:p ≤ 0.84 and HA:p > 0.84 D. H0:p ≥ 0.84 and HA:p < 0.84 32. A professional sports organization is going to implement a test for steroids. The test gives a positive reaction in 94% of the people who have taken the steroid. However, it erroneously gives a positive reaction in 4% of the people who have not taken the steroid. What is the probability of Type I and Type II errors giving the null hypothesis "the individual has not taken steroids." A. Type I: 4%, Type II: 6% B. Type I: 6%, Type II: 4% C. Type I: 94%, Type II: 4% D. Type I: 4%, Type II: 94% 38. Consider the following hypotheses that relate to the medical field: Ho: A person is free of disease. HA: A person has disease. In this instance, a Type I error is often referred to as ___________. A. a false positive B. a false negative C. a negative result D. the power of the test 39. Consider the following hypotheses that relate to the medical field: Ho: A person is free of disease. HA: A person has disease. In this instance, a Type II error is often referred to as ___________. A. a false positive B. a false negative C. a negative result D. the power of the test 40. A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: Ho: μ ≤ 300. HA: μ > 300. The consequences of committing a Type I error would be that____________________________. A. the franchiser builds on an acceptable site B. the franchiser builds on an unacceptable site C. the franchiser does not build on an acceptable site D. the franchiser does not build on an unacceptable site 41. A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: Ho: μ ≤ 300. HA: μ > 300. The consequences of committing a Type II error would be that__________________________. A. the franchiser builds on an acceptable site B. the franchiser builds on an unacceptable site C. the franchiser does not build on an acceptable site D. the franchiser does not build on an unacceptable site 42. A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. If the advisor tests the hypotheses Ho: μ ≤ 300 versus HA: μ > 300, μ stands for ____________. A. the average number of automobiles that pass the intersection per hour B. the number of automobiles that pass the intersection per hour C. the proportion of automobiles that pass the intersection per hour D. the standard deviation of the number of automobiles that pass the intersection per hour 48. When conducting a hypothesis test concerning the population proportion, the value of the test statistic is calculated as ____________. A. B. C. D. 49. Which of the following represents an appropriate set of hypotheses? A. B. C. D. 50. If the chosen significance level is α = 0.05, then ____________________________________________. A. there is a 5% probability of rejecting a true null hypothesis B. there is a 5% probability of accepting a true null hypothesis C. there is a 5% probability of rejecting a false null hypothesis D. there is a 5% probability of accepting a false null hypothesis 51. When conducting a hypothesis test for a given sample size, if a is increased from 0.05 to 0.10, then __________________. A. the probability of incorrectly rejecting the null hypothesis increases B. the probability of incorrectly failing to reject the null hypothesis decreases C. the probability of Type II error decreases D. All of the above 52. When conducting a hypothesis test for a given sample size, if the probability of a Type I error decreases, then the ______________________________________. A. probability of Type II error decreases B. probability of incorrectly rejecting the null hypothesis increases C. probability of incorrectly accepting the null hypothesis increases D. probability of incorrectly accepting the null hypothesis decreases 53. Which of the following are one-tailed tests? A. Ho:μ ≤ 10, HA:μ > 10 B. Ho:μ = 10, HA:μ ≠ 10 C. Ho:μ ≥ 400, HA:μ < 400 D. Both Ho:μ ≤ 10, HA:μ > 10 and Ho:μ ≥ 400, HA:μ < 400 54. Which of the following are two-tailed tests? A. Ho:μ ≤ 10, HA:μ > 10 B. Ho:μ = 10, HA:μ ≠ 10 C. Ho:μ ≥ 400, HA:μ < 400 D. Both Ho:μ ≤ 10, HA:μ > 10 and Ho:μ ≥ 400, HA:μ < 400 60. A one-tailed hypothesis test of the population mean has ______________. A. only one critical value B. two critical values, both positive C. two critical values, both negative D. two critical values, one positive and one negative 61. Consider the following competing hypotheses: Ho:μ = 0, HA:μ ≠ 0. The value of the test statistic is z = −1.38. If we choose a 5% significance level, then we ___________________________________________. A. reject the null hypothesis and conclude that the population mean is significantly different from zero B. reject the null hypothesis and conclude that the population mean is not significantly different from zero C. do not reject the null hypothesis and conclude that the population mean is significantly different from zero D. do not reject the null hypothesis and conclude that the population mean is not significantly different from zero 62. A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. The parameter to be tested is ___________________________. A. the mean GPA of all university students B. the mean GPA of the university honors students C. the mean GPA of 3.60 for the 36 selected honors students D. the proportion of honors students with a GPA exceeding 3.50 63. A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. To establish whether the mean GPA exceeds 3.50, the appropriate hypotheses are ______________. A. B. C. D. 64. A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. The value of the test statistic is ____________. A. z = – 1.50 B. t35 = – 1.50 C. z = 1.50 D. t35 = 1.50 65. A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. At a 5% significance level, the critical value(s) is(are) ________. A. 1.64 5 B. 1.69 0 C. –1.96 and 1.96 D. –2.030 and 2.030 66. A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. At a 5% significance level, the decision is to _____________. A. reject Ho we can conclude that the mean GPA is significantly greater than 3.50 B. reject Ho we cannot conclude that the mean GPA is significantly greater than 3.50 C. not reject Ho we can conclude that the mean GPA is significantly greater than 3.50 D. not reject Ho we cannot conclude that the mean GPA is significantly greater than 3.50 70. The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350. At a 5% significance level, the critical value(s) is(are) ___________. A. 1.64 5 B. – 1.645 C. –1.96 and 1.96 D. –2.030 and 2.030 71. The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350. At the 5% significance level, the decision is to ___________. A. reject Ho; we can conclude that the mean number of customers visiting the dealership is significantly less than 800 B. reject Ho; we cannot conclude that the mean number of customers visiting the dealership is significantly less than 800 C. do not reject Ho; we can conclude that the mean number of customers visiting the dealership is significantly less than 800 D. do not reject Ho;we cannot conclude that the mean number of customers visiting the dealership is significantly less than 800 72. The Boston public school district has had difficulty maintaining on-time bus service for its students ("A Year Later, School Buses Still Late," Boston Globe, October 5, 2011). Suppose the district develops a new bus schedule to help combat chronic lateness on a particularly woeful route. Historically, the bus service on the route has been, on average, 12 minutes late. After the schedule adjustment, the first 36 runs were an average of eight minutes late. As a result, the Boston public school district claimed that the schedule adjustment was an improvement—students were not as late. Assume a population standard deviation for bus arrival time of 12 minutes. Which of the following can be used to determine whether the schedule adjustment reduced the average lateness time of 12 minutes? A. B. C. D. 75. The Boston public school district has had difficulty maintaining on-time bus service for its students ("A Year Later, School Buses Still Late," Boston Globe, October 5, 2011). Suppose the district develops a new bus schedule to help combat chronic lateness on a particularly woeful route. Historically, the bus service on the route has been, on average, 12 minutes late. After the schedule adjustment, the first 36 runs were an average of eight minutes late. As a result, the Boston public school district claimed that the schedule adjustment was an improvement—students were not as late. Assume a population standard deviation for bus arrival time of 12 minutes. At the 1% significance level, does the evidence support the Boston public schools’ claim? A. No, because the p-value is greater than α. B. Yes, because thep-value is greater than α. C. No, because the value of the test statistic is less than the critical value. D. Yes, because the value of the test statistic is less than the critical value. 76. An analyst conducts a hypothesis test to check whether the mean return for a particular fund differs from 10%. He assumes that returns are normally distributed and sets up the following competing hypotheses: Ho:μ = 10,HA:μ ≠ 10 Over the past 10 years the fund has had an average annual return of 13.4% with a standard deviation of 2.6%. The value of the test statistic is 4.14 and the critical values at the 5% significance level are−2.262 and 2.262.The correct decision is to ____________________________________. A. reject Ho; we can conclude that the mean differs from 10% B. reject Ho; we cannot conclude that the mean differs from 10% C. not reject Ho; we can conclude that the mean differs from 10% D. not reject Ho; we cannot conclude that the mean differs from 10% 77. A 99% confidence interval for the population mean yields the following results: [−3.79, 5.86].At the 1% significance level, what decision should be made regarding the following hypothesis test with Ho:μ = 0,HA:μ ≠ 0? A. Reject Ho; we can conclude that the mean differs from zero. B. Reject Ho; we cannot conclude that the mean differs from zero. C. Do not reject Ho; we can conclude that the mean differs from zero. D. Do not reject Ho; we cannot conclude that the mean differs from zero. 78. To test if the mean IQ of employees in an organization is greater than 100, a sample of 30 employees is taken and the value of the test statistic is computed as t29 = 2.42 If we choose a 5% significance level, we _____________. A. reject the null hypothesis and conclude that the mean IQ is greater than 100 B. reject the null hypothesis and conclude that the mean IQ is not greater than 100 C. do not reject the null hypothesis and conclude that the mean IQ is greater than 100 D. do not reject the null hypothesis and conclude that the mean IQ is not greater than 100 83. A schoolteacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L. The school samples the air for 36 days and finds an average concentration of 4.4pCi/L with a standard deviation of 1pCi/L. At a 5% significance level, the critical value(s) is(are) _______. A. −1.69 0 B. 1.69 0 C. −1.96 and 1.96 D. −2.030 and 2.030 84. A schoolteacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L. The school samples the air for 36 days and finds an average concentration of 4.4pCi/L with a standard deviation of 1pCi/L. At a 5% significance level, the decision is to ________________________________________________. A. reject Ho; we can conclude that the mean concentration of radon gas is greater than the safe level B. reject Ho; we cannot conclude that the mean concentration of radon gas is greater than the safe level C. not reject Ho; we can conclude that the mean concentration of radon gas is greater than the safe level D. not reject Ho; we cannot conclude that the mean concentration of radon gas is greater than the safe level 85. A car dealer who sells only late-model luxury cars recently hired a new salesperson and believes that this salesperson is selling at lower markups. He knows that the long-run average markup in his lot is $5,600. He takes a random sample of 16 of the new salesperson’s sales and finds an average markup of $5,000 and a standard deviation of $800. Assume the markups are normally distributed. What is the value of an appropriate test statistic for the car dealer to use to test his claim? A. t15 = – 3.00 B. z = – 3.00 C. t15 = – 0.75 D. z = – 0.75 86. A manager at a temp agency believes that one of the agency’s recruiters has unorthodox methods and claims that the wages the recruiter secures for its temps differ from the agency’s average wage of $12 per hour. The agency takes a random sample of 49 recent contracts the recruiter secured and finds an average wage of $11.25 per hour and a standard deviation of $2.25 per hour. Does the evidence support the agency’s claim at the 5% significance level? A. Yes, because the p-value is greater than α, the claim is supported. B. No, because the p-value is not greater than α, the claim is not supported. C. Yes, because the value of the test statistic is less than the critical value, the claim is supported. D. No, because the value of the test statistic is greater than the critical value, the claim is not supported. 87. A newly hired basketball coach promised a high-paced attack that will put more points on the board than the team’s previously tepid offense historically managed. After a few months, the team owner looks at the data to test the coach’s claim. He takes a sample of 36 of the team’s games under the new coach and finds that they scored an average of 101 points with a standard deviation of 6 points. Over the past 10 years, the team had averaged 99 points. What is(are) the appropriate critical value(s) to test the new coach’s claim at the 1% significance level? A. −2.43 8 B. −2.438 and 2.438 C. 2.32 6 D. 2.43 8 88. A newly hired basketball coach promised a high-paced attack that will put more points on the board than the team’s previously tepid offense historically managed. After a few months, the team owner looks at the data to test the coach’s claim. He takes a sample of 36 of the team’s games under the new coach and finds that they scored an average of 101 points with a standard deviation of 6 points. Over the past 10 years, the team had averaged 99 points. What is the value of the appropriate test statistic to test the new coach’s claim at the 1% significance level? A. t35 = 0.33 B. z = 0.33 C. t35 = 2.00 D. z = 2.00 93. A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 200 graduates, 30 students have a GPA of 3.00 or below. The value of the test statistic and its associated p-value are ________________________. A. t199 = –1.77 and p-value = 0.0384 B. z = –1.77 and p-value = 0.0384 C. t199 = –1.77 and p-value = 0.0768 D. z = –1.77 and p-value = 0.0768 94. A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 200 graduates, 30 students have a GPA of 3.00 or below. At a 5% significance level, the decision is to _________________________________________________________________________.. A. reject Ho; we can conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20 B. reject Ho; we cannot conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20 C. not reject Ho; we can conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20 D. not reject Ho; we cannot conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20 95. The Institute of Education Sciences measures the high school dropout rate as the percentage of 16-through 24-year-olds who are not enrolled in school and have not earned a high school credential. In 2009, the high school dropout rate was 8.1%. A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. When testing whether the dropout rate has decreased, the appropriate hypotheses are _____________. A. B. C. D. 98. The Institute of Education Sciences measures the high school dropout rate as the percentage of 16- through 24-year-olds who are not enrolled in school and have not earned a high school credential. In 2009, the high school dropout rate was 8.1%. A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. At a 5% significance level, the decision is to ____________. A. reject Ho; we can conclude that the high school dropout rate has decreased B. reject Ho; we cannot conclude that the high school dropout rate has decreased C. do not reject Ho; we can conclude that the high school dropout rate has decreased D. do not reject Ho; we cannot conclude that the high school dropout rate has decreased 99. Vermont-based Green Mountain Coffee Roasters dominates the market for single- serve coffee in the United States, with its subsidiary Keurig accounting for approximately 70% of sales ("Rivals Try to Loosen Keurig’s Grip on Single-Serve Coffee Market," Chicago Tribune, February 26, 2011). But Keurig’s patent on K-cups, the plastic pods used to brew the coffee, is expected to expire in 2012, allowing other companies to better compete. Suppose a potential competitor has been conducting blind taste tests on its blend and finds that 47% of consumers strongly prefer its French Roast to that of Green Mountain Coffee Roasters. After tweaking its recipe, the competitor conducts a test with 144 tasters, of which 72 prefer its blend. The competitor claims that its new blend is preferred by more than 47% of consumers to Green Mountain Coffee Roasters’ French Roast. Which of the following should be used to develop the null and alternative hypotheses to test this claim? A. B. C. D. 100 . Vermont-based Green Mountain Coffee Roasters dominates the market for single- serve coffee in the United States, with its subsidiary Keurig accounting for approximately 70% of sales ("Rivals Try to Loosen Keurig’s Grip on Single-Serve Coffee Market," Chicago Tribune, February 26, 2011). But Keurig’s patent on K-cups, the plastic pods used to brew the coffee, is expected to expire in 2012, allowing other companies to better compete. Suppose a potential competitor has been conducting blind taste tests on its blend and finds that 47% of consumers strongly prefer its French Roast to that of Green Mountain Coffee Roasters. After tweaking its recipe, the competitor conducts a test with 144 tasters, of which 72 prefer its blend. The competitor claims that its new blend is preferred by more than 47% of consumers to Green Mountain Coffee Roasters’ French Roast. What is the value of the appropriate test statistic to test this claim? A. t143 = 0.721 B. z = 0.721 C. t143 = 1.96 D. z = 1.96 104 . Expedia would like to test if the average round-trip airfare between Philadelphia and Dublin is less than $1,200. Which of the following hypothesis tests should be performed? A. Left- tailed B. Right- tailed C. Two- tailed D. There is not enough information to answer. 105 . A company has developed a new diet that it claims will lower one’s weight by more than 10 pounds. Health officials decide to conduct a test to validate this claim. The manager of the company _____________________________________. A. is more concerned about Type I error B. is more concerned about Type II error C. is concerned about both Type I and Type II errors D. is not concerned at all 106 . A company has developed a new diet that it claims will lower one’s weight by more than 10 pounds. Health officials decide to conduct a test to validate this claim. The consumers should be _____________________________________. A. more concerned about Type I error B. more concerned about Type II error C. concerned about both Type I and Type II errors D. is not concerned at all 107 . A company decided to test the hypothesis that the average time a company’s employees are spending to check their private e-mails at work is more than 6 minutes. A random sample of 40 employees were selected and they averaged 6.6 minutes. It is believed that the population standard deviation is 1.7 minutes. The α is set to 0.05. The p-value for this hypothesis test would be ______. A. 0.064 4 B. 0.012 9 C. 0.026 8 D. 0.039 5 108 . A company decided to test the hypothesis that the average time a company’s employees are spending to check their private e-mails at work is more than 6 minutes. A random sample of 40 employees were selected and they averaged 6.6 minutes. It is believed that the population standard deviation is 1.7 minutes. The α is set to 0.05. The critical value for this hypothesis test would be ______. A. 6. 0 B. 7. 4 C. 6. 4 D. 7. 9 109 . The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor’s degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The α is set to 0.05. The confidence interval for this hypothesis test would be __________________. A. [$14,118.9, $19,881.2] B. [$14,839.1, $19,160.9] C. [$16,279.7, $17,720.3] D. [$15,588.2, $18,411.8] 110 . The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor’s degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The α is set to 0.05. The p-value for this hypothesis test would be ______. A. 0.131 0 B. 0.095 0 C. 0.047 5 D. 0.021 9 115 . A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. If this is to happen, it will have to move one of its most viewed shows to another slot. The network conducts a survey asking its viewers which show they would rather watch. The network receives 827 responses, of which 428 indicate that they would like to see the new show in the lineup. The test statistic for this hypothesis would be _______. A. 1.3 5 B. 1.0 5 C. 1.2 5 D. 1.1 5 116 . A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. If this is to happen, it will have to move one of its most viewed shows to another slot. The network conducts a survey asking its viewers which show they would rather watch. The network receives 827 responses, of which 428 indicate that they would like to see the new show in the lineup. At the 1% significance level, the rejection region(s) for this hypothesis would be ________. A. 2.33 0 B. 2.03 0 C. 1.96 0 D. 1.64 5 117 . Construct the null and alternative hypotheses for the following claims. a. "The school’s mean GPA differs from 2.50 GPA." b. "The school’s mean GPA is less than 2.50 GPA." 118 . Massachusetts Institute of Technology grants pirate certificates to those students who successfully complete courses in archery, fencing, sailing, and pistol shooting ("MIT Awards Pirate Certificates to Undergraduates," Boston Globe, March 3, 2012). Sheila claims that those students who go on to earn pirate certificates are able to hit a higher proportion of bull’s-eyes during the archery final exam than the course average of 0.15. Specify the null and alternative hypotheses to test her claim. 119 . An engineer is designing an experiment to test if airplane engines are faulty and unsafe to fly. The engineer expects 0.0001% of engines to be unsafe. The null hypothesis is that the probability of an unsafe engine is less than or equal to 0.0001% and the alternative hypothesis is that the probability the engine is unsafe is greater than 0.0001%. a. Describe the consequences of Type I and Type II errors. b. Should the engineer design the test with a higher alpha or a higher beta? Explain. 120 . George W. Bush famously claimed in his 2003 State of the Union address that the United States had uncovered evidence that Iraq had developed weapons of mass destruction under Saddam Hussein. Consider the null hypothesis, "Iraq does not possess weapons of mass destruction." After deciding that Iraq did possess weapons of mass destruction and invading this country, the United States found no evidence of said weapons. Is this a Type I or a Type II error on the part of the United States? Explain. 123 . An engineer wants to know if the average amount of energy used in his factory per day has changed since 2005. The factory used an average of 2,000 megawatt hours (mwh) per day prior to 2005. Since 2005, the engineer surveyed 400 days and found the average energy use was 2,040 mwh per day. Assume that the population standard deviation is 425 mwh per day. a. Specify the null and alternative hypotheses to determine whether the factory’s energy use has changed. b. Calculate the value of the test statistic and the p-value. c. At the 5% significance level, can you conclude that the energy usage has changed? Explain. 124 . A university wants to know if the average salary of its graduates has increased since 2010. The average salary of graduates prior to 2010 was $48,000. Since 2010, the university surveyed 256 graduates and found an average salary of $48,750. Assume that the standard deviation of all graduates’ salaries is $7,000. a. Specify the null and alternative hypotheses to determine whether the average salary of graduates has increased. b. Calculate the value of the test statistic and the critical value at a 5% significance level. c. At the 5% significance level, can you conclude that salaries have increased? Explain. 125 . Students who graduated from college in 2010 with student loans owed an average of $25,250 (TheNew York Times, November 2, 2011). An economist wants to determine if the average debt has increased since 2010. She takes a sample of 40 recent graduates and finds that their average debt was $28,275. Assume that the population standard deviation is $7,250. a. Specify the competing hypotheses to determine whether the average undergraduate debt has increased since 2001. b. Calculate the value of the test statistic and the p-value. c. At the 5% significance level, can you conclude that the average undergraduate debt has increased? Explain. 128 . A city is considering widening a busy intersection in town. Last year, the city reported 16,000 cars passed through the intersection per day. The city conducted a survey for 49 days this year and found an average of 17,000 cars passed through the intersection, with a standard deviation of 5,000. a. Specify the null and alternative hypotheses to determine whether the intersection has seen an increase in traffic. b. Calculate the value of the test statistic and approximate the p-value. c. The city is going to widen the intersection if it believes traffic has increased. At the 5% significance level, can you conclude that the intersection has seen an increase in traffic? Should the city widen the intersection? 129 . A hairdresser believes that she is more profitable on Tuesdays, her lucky day of the week. She knows that, on average, she has a daily revenue of $250. She randomly samples the revenue from eight Tuesdays and finds she takes in $260, $245, $270, $260, $295, $235, $270, and $265. Assume that daily revenue is normally distributed. a. Specify the population parameter to be tested. b. Specify the null and alternative hypotheses to test the hairdresser’s claim. c. Calculate the sample mean revenue and the sample standard deviation. d. Compute the value of the appropriate test statistic. e. At the 10% significance level, specify the critical value(s). f. At the 10% significance level, is the hairdresser’s claim supported by the data? 130 . A portfolio manager claims that the mean annual return on one of the mutual funds he manages exceeds 8%. To substantiate his claim, he states that over the past 10 years, the mean annual return for the mutual fund has been 9.5% with a sample standard deviation of 1.5%. Assume annual returns are normally distributed. a. Specify the competing hypotheses to test the portfolio manager’s claim. b. Calculate the value of the test statistic. c. At the 5% significance level, use the critical value approach to state the decision rule. d. Is the portfolio manager’s claim substantiated by the data? Explain. 133 . A doctor thinks he has found a miraculous cure for rheumatoid arthritis. He thinks it will cure more than 50% of all cases within a year of first taking the drug. To test his drug, he runs a clinical trial on 400 patients with rheumatoid arthritis. He finds that 208 of the patients are symptomfree within a year. a. Specify the null and alternative hypotheses to determine whether the proportion of patients that are cured by the drug exceeds 50%. b. Calculate the value of the test statistic, and find the critical value at a 5% significance level. c. At the 5% significance level, can you conclude that the percentage of patients who are cured by the drug exceeds 50%? 134 . The percentage of complete passes is an important measure for a quarterback in the NFL. A particular quarterback has a career completion percentage of 55%. The quarterback got a new coach and then played a few games where he completed 48 of 100 passes. a. Specify the null and alternative hypotheses to determine whether the proportion of completed passes has decreased with the new coach. b. Calculate the value of the test statistic and the p-value. c. At the 5% significance level, can you conclude that the quarterback’s completion percentage has decreased? 135 . A Massachusetts state police officer measured the speed of 100 motorists on the Massachusetts Turnpike and found that 70 exceeded the posted speed limit by more than 10 miles per hour. The police officer claims that more than 60% of motorists drive at least 10 miles per hour more than the posted speed on the turnpike. a. Specify the null and alternative hypotheses to test the officer’s claim. b. Calculate the value of the test statistic. c. At the 5% significance level, what is(are) the critical value(s) to test the officer’s claim? d. At the 5% significance level, does the evidence support the officer’s claim? Accessibility: Keyboard Navigation Blooms: Remember Difficulty: 1 Easy Jaggia - Chapter 09 #6 Learning Objective: 09-02 Distinguish between Type I and Type II errors. Topic: Introduction to Hypothesis Testing 7. A Type II error is made when we reject the null hypothesis and the null hypothesis is actually false. FALSE A Type II error is made when we do not reject the null hypothesis that is actually false. AACSB: Analytical Thinking Accessibility: Keyboard Navigation Blooms: Remember Difficulty: 1 Easy Jaggia - Chapter 09 #7 Learning Objective: 09-02 Distinguish between Type I and Type II errors. Topic: Introduction to Hypothesis Testing 8. For a given sample size, any attempt to reduce the likelihood of making one type of error (Type I or Type II) will increase the likelihood of the other error. TRUE It is not always easy to determine which of two errors has more serious consequences. For a given evidence, there is a trade-off between these errors; by reducing Type I error, we implicitly increase Type II error, and vice versa. AACSB: Analytical Thinking Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 2 Medium Jaggia - Chapter 09 #8 Learning Objective: 09-02 Distinguish between Type I and Type II errors. Topic: Introduction to Hypothesis Testing 9. A hypothesis test regarding the population mean µ is based on the sampling distribution of the sample mean TRUE A hypothesis test regarding the population mean µ is based on the sampling distribution of the sample mean AACSB: Analytical Thinking Blooms: Understand Difficulty: 2 Medium Jaggia - Chapter 09 #9 Learning Objective: 09-03 Conduct a hypothesis test using the p-value approach. Topic: Hypothesis Test for the Population Mean When σ Is Known 10. Under the assumption that the null hypothesis is true as an equality, the p-value is the likelihood of observing a sample mean that is at least as extreme as the one derived from the given sample. TRUE The <i>p-</i>value is the likelihood of obtaining a sample mean that is at least as extreme as the one derived from the given sample, under the assumption that the null hypothesis is true as an equality. AACSB: Analytical Thinking Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 2 Medium Jaggia - Chapter 09 #10 Learning Objective: 09-03 Conduct a hypothesis test using the p-value approach. Topic: Hypothesis Test for the Population Mean When σ Is Known 11. The critical value approach specifies a range of values, also called the rejection region, such that if the value of the test statistic falls into this range, we do not reject the null hypothesis. FALSE The critical value approach specifies a range of values, also called the rejection region, such that if the value of the test statistic falls into this range, we reject the null hypothesis. AACSB: Analytical Thinking Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 2 Medium Jaggia - Chapter 09 #11 Learning Objective: 09-04 Conduct a hypothesis test using the critical value approach. Topic: Hypothesis Test for the Population Mean When σ Is Known 12. The hypothesis statement H: µ = 25 is an example of a(an) ________ hypothesis. null In general, the null hypothesis regarding a particular population parameter of interest is specified with one of the following signs: =, ≥, ≤; the alternative hypothesis is then specified with the corresponding opposite sign: ≠, >, <. AACSB: Analytical Thinking Blooms: Remember Difficulty: 1 Easy Jaggia - Chapter 09 #12 Learning Objective: 09-03 Conduct a hypothesis test using the p-value approach. Topic: Introduction to Hypothesis Testing 20. Excel’s function _______ returns the p-value for a right-tailed test. Z.TEST Excel’s function Z.TEST returns the p-value for a right-tailed test, or equivalently P(Z ≥ z). AACSB: Analytical Thinking Blooms: Understand Difficulty: 2 Medium Jaggia - Chapter 09 #20 Learning Objective: 09-04 Conduct a hypothesis test using the critical value approach. Topic: Hypothesis Test for the Population Mean When σ Is Known 21. To obtain the p-value for a right-tailed test of the population mean, when σ is unknown, we use the Excel’s function _________. T.DIST.RT To obtain the p-value for a right-tailed test of the population mean, when σ is unknown, we use the Excel’s function T.DIST.RT. AACSB: Analytical Thinking Blooms: Understand Difficulty: 2 Medium Jaggia - Chapter 09 #21 Learning Objective: 09-05 Differentiate between the test statistics for the population mean. Topic: Hypothesis Test for the Population Mean When σ Is Unknown 22. The null hypothesis in a hypothesis test refers to _____________. A. the desired outcome B. the default state of nature C. the altered state of nature D. the desired state of nature AACSB: Analytical Thinking Accessibility: Keyboard Navigation Blooms: Remember Difficulty: 1 Easy Jaggia - Chapter 09 #22 Learning Objective: 09-01 Define the null hypothesis and the alternative hypothesis. Topic: Introduction to Hypothesis Testing 23. In general, the null and alternative hypotheses are __________. A. additiv e B. correlat ed C. multiplicati ve D. mutually exclusive AACSB: Analytical Thinking Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 2 Medium Jaggia - Chapter 09 #23 Learning Objective: 09-01 Define the null hypothesis and the alternative hypothesis. Topic: Introduction to Hypothesis Testing 24. The alternative hypothesis typically ___________. A. corresponds to the presumed default state of nature B. contests the status quo, for which a corrective action may be required C. states the probability of rejecting the null hypothesis when it is false D. states the probability of rejecting the null hypothesis when it is true AACSB: Analytical Thinking Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 2 Medium Jaggia - Chapter 09 #24 Learning Objective: 09-01 Define the null hypothesis and the alternative hypothesis. Topic: Introduction to Hypothesis Testing 25. Which of the following types of tests may be performed? A. Right-tailed and two-tailed tests B. Left-tailed and two-tailed tests C. Right-tailed and left-tailed tests D. Right-tailed, left-tailed, and two- tailed tests AACSB: Analytical Thinking Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 2 Medium Jaggia - Chapter 09 #25 Learning Objective: 09-01 Define the null hypothesis and the alternative hypothesis. Topic: Introduction to Hypothesis Testing 26. The national average for an eighth-grade reading comprehension test is 73. A school district claims that its eighth-graders outperform the national average. In testing the school district’s claim, how does one define the population parameter of interest? A. The mean score on the eighth-grade reading comprehension test B. The number of eighth graders who took the reading comprehension test C. The standard deviation of the score on the eighth-grade reading comprehension test D. The proportion of eighth graders who scored above 73 on the reading comprehension test AACSB: Analytical Thinking Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 2 Medium Jaggia - Chapter 09 #26 Learning Objective: 09-01 Define the null hypothesis and the alternative hypothesis. Topic: Introduction to Hypothesis Testing 30. It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. Identify the correct null and alternative hypotheses to test the politician’s claim. A. H0:p = 0.50 and HA:p ≠ 0.50 B. H0:p ≤ 0.50 and HA:p > 0.50 C. H0:p ≥ 0.50 and HA:p > 0.50 D. H0:p ≥ 0.50 and HA:p < 0.50 AACSB: Analytical Thinking Blooms: Understand Difficulty: 2 Medium Jaggia - Chapter 09 #30 Learning Objective: 09-01 Define the null hypothesis and the alternative hypothesis. Topic: Introduction to Hypothesis Testing 31. Many cities around the United States are installing LED streetlights, in part to combat crime by improving visibility after dusk. An urban police department claims that the proportion of crimes committed after dusk will fall below the current level of 0.84 if LED streetlights are installed. Specify the null and alternative hypotheses to test the police department’s claim. A. H0:p = 0.84 and HA:p ≠ 0.84 B. H0:p < 0.84 and HA:p ≥ 0.84 C. H0:p ≤ 0.84 and HA:p > 0.84 D. H0:p ≥ 0.84 and HA:p < 0.84 AACSB: Analytical Thinking Blooms: Understand Difficulty: 2 Medium Jaggia - Chapter 09 #31 Learning Objective: 09-01 Define the null hypothesis and the alternative hypothesis. Topic: Introduction to Hypothesis Testing 32. A professional sports organization is going to implement a test for steroids. The test gives a positive reaction in 94% of the people who have taken the steroid. However, it erroneously gives a positive reaction in 4% of the people who have not taken the steroid. What is the probability of Type I and Type II errors giving the null hypothesis "the individual has not taken steroids." A. Type I: 4%, Type II: 6% B. Type I: 6%, Type II: 4% C. Type I: 94%, Type II: 4% D. Type I: 4%, Type II: 94% AACSB: Analytical Thinking Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 3 Hard Jaggia - Chapter 09 #32 Learning Objective: 09-02 Distinguish between Type I and Type II errors. Topic: Introduction to Hypothesis Testing 33. A statistics professor works tirelessly to catch students cheating on his exams. He has particular routes for his teaching assistants to patrol, an elevated chair to ensure an unobstructed view of all students, and even a video recording of the exam in case additional evidence needs to be collected. He estimates that he catches 95% of students who cheat in his class, but 1% of the time that he accuses a student of cheating he is actually incorrect. Consider the null hypothesis, "the student is not cheating." What is the probability of a Type I error? A. 1 % B. 5 % C. 95 % D. 99 % AACSB: Analytical Thinking Accessibility: Keyboard Navigation Blooms: Apply Difficulty: 3 Hard Jaggia - Chapter 09 #33 Learning Objective: 09-02 Distinguish between Type I and Type II errors. Topic: Introduction to Hypothesis Testing 34. A Type I error occurs when we ___________. A. reject the null hypothesis when it is actually true B. reject the null hypothesis when it is actually false C. do not reject the null hypothesis when it is actually true D. do not reject the null hypothesis when it is actually false AACSB: Analytical Thinking Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 2 Medium Jaggia - Chapter 09 #34 Learning Objective: 09-02 Distinguish between Type I and Type II errors. Topic: Introduction to Hypothesis Testing 38. Consider the following hypotheses that relate to the medical field: Ho: A person is free of disease. HA: A person has disease. In this instance, a Type I error is often referred to as ___________. A. a false positive B. a false negative C. a negative result D. the power of the test AACSB: Analytical Thinking Blooms: Understand Difficulty: 2 Medium Jaggia - Chapter 09 #38 Learning Objective: 09-02 Distinguish between Type I and Type II errors. Topic: Introduction to Hypothesis Testing 39. Consider the following hypotheses that relate to the medical field: Ho: A person is free of disease. HA: A person has disease. In this instance, a Type II error is often referred to as ___________. A. a false positive B. a false negative C. a negative result D. the power of the test AACSB: Analytical Thinking Blooms: Understand Difficulty: 2 Medium Jaggia - Chapter 09 #39 Learning Objective: 09-02 Distinguish between Type I and Type II errors. Topic: Introduction to Hypothesis Testing 40. A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: Ho: μ ≤ 300. HA: μ > 300. The consequences of committing a Type I error would be that____________________________. A. the franchiser builds on an acceptable site B. the franchiser builds on an unacceptable site C. the franchiser does not build on an acceptable site D. the franchiser does not build on an unacceptable site AACSB: Analytical Thinking Blooms: Apply Difficulty: 3 Hard Jaggia - Chapter 09 #40 Learning Objective: 09-02 Distinguish between Type I and Type II errors. Topic: Introduction to Hypothesis Testing 44. When conducting a hypothesis test, which of the following decisions represents an error? A. Rejecting the null hypothesis when it is true. B. Rejecting the null hypothesis when it is false. C. Not rejecting the null hypothesis when it is true. D. Rejecting the null hypothesis when it is false and not rejecting the null hypothesis when it is true. AACSB: Analytical Thinking Accessibility: Keyboard Navigation Blooms: Understand Difficulty: 2 Medium Jaggia - Chapter 09 #44 Learning Objective: 09-02 Distinguish between Type I and Type II errors. Topic: Introduction to Hypothesis Testing 45. A hypothesis test regarding the population mean is based on ________________________________. A. the sampling distribution of the sample mean B. the sampling distribution of the sample variance C. the sampling distribution of the sample proportion D. the sampling distribution of the sample standard deviation AACSB: Analytical Thinking Blooms: Understand Difficulty: 2 Medium Jaggia - Chapter 09 #45 Learning Objective: 09-03 Conduct a hypothesis test using the p-value approach. Topic: Introduction to Hypothesis Testing 46. When conducting a hypothesis test concerning the population mean, and the population standard deviation is known, the value of the test statistic is calculated as _________. A. B. C. D. AACSB: Analytical Thinking Blooms: Understand Difficulty: 2 Medium Jaggia - Chapter 09 #46 Learning Objective: 09-03 Conduct a hypothesis test using the p-value approach. Topic: Hypothesis Test for the Population Mean When σ Is Known 47. When conducting a hypothesis test concerning the population mean, and the population standard deviation is unknown, the value of the test statistic is calculated as __________. A. B. C. D. AACSB: Analytical Thinking Blooms: Understand Difficulty: 2 Medium Jaggia - Chapter 09 #47 Learning Objective: 09-05 Differentiate between the test statistics for the population mean. Topic: Hypothesis Test for the Population Mean When σ Is Unknown 48. When conducting a hypothesis test concerning the population proportion, the value of the test statistic is calculated as ____________. A. B. C. D. AACSB: Analytical Thinking Blooms: Understand