商务统计学 第九章习题.doc

CHAPTER 9: FUNDAMENTALS OF HYPOTHESIS TESTING: ONE-SAMPLE TESTS1. Which of the following would be an appropriate null hypothesis?a) The mean of a population is equal to 55. b) The mean of a sample is equal to 55.c) The mean of a population is greater than 55.d) Only (a) and (c) are true.ANSWER:aTYPE: MC DIFFICULTY: Easy KEYWORDS: form of hypothesis2. Which of the following would be an appropriate null hypothesis?a) The population proportion is less than 0.65. b) The sample proportion is less than 0.65.c) The population proportion is no less than 0.65.d) The sample proportion is no less than 0.65.ANSWER:cTYPE: MC DIFFICULTY: Easy KEYWORDS: form of hypothesis3. Which of the following would be an appropriate alternative hypothesis?a) The mean of a population is equal to 55. b) The mean of a sample is equal to 55.c) The mean of a population is greater than 55.d) The mean of a sample is greater than 55.ANSWER:cTYPE: MC DIFFICULTY: Easy KEYWORDS: form of hypothesis4. Which of the following would be an appropriate alternative hypothesis?a) The population proportion is less than 0.65. b) The sample proportion is less than 0.65.c) The population proportion is no less than 0.65.d) The sample proportion is no less than 0.65.ANSWER:aTYPE: MC DIFFICULTY: Easy KEYWORDS: form of hypothesis5. A Type II error is committed whena) we reject a null hypothesis that is true.b) we don't reject a null hypothesis that is true.c) we reject a null hypothesis that is false.d) we don't reject a null hypothesis that is false.ANSWER:dTYPE: MC DIFFICULTY: EasyKEYWORDS: type II error 6. A Type I error is committed whena) we reject a null hypothesis that is true.b) we don't reject a null hypothesis that is true.c) we reject a null hypothesis that is false.d) we don't reject a null hypothesis that is false.ANSWER:aTYPE: MC DIFFICULTY: Easy KEYWORDS: type I error7. The power of a test is measured by its capability ofa) rejecting a null hypothesis that is true.b) not rejecting a null hypothesis that is true.c) rejecting a null hypothesis that is false.d) not rejecting a null hypothesis that is false.ANSWER:cTYPE: MC DIFFICULTY: Easy KEYWORDS: power8. True or False: For a given level of significance, if the sample size is increased, the power of the test will increase.ANSWER:TrueTYPE: TF DIFFICULTY: Moderate KEYWORDS: power, level of significance, sample size9. True or False: For a given level of significance, if the sample size is increased, the probability of committing a Type I error will increase.ANSWER:FalseTYPE: TF DIFFICULTY: Moderate KEYWORDS: level of significance, sample size, type I error10. True or False: For a given level of significance, if the sample size is increased, the probability of committing a Type II error will increase.ANSWER:FalseTYPE: TF DIFFICULTY: Moderate KEYWORDS: level of significance, sample size, type II error11. True or False: For a given sample size, the probability of committing a Type II error will increase when the probability of committing a Type I error is reduced.ANSWER:TrueTYPE: TF DIFFICULTY: Moderate KEYWORDS: sample size, type I error, type II error12. If an economist wishes to determine whether there is evidence that average family income in a community exceeds $25,000a) either a one-tailed or two-tailed test could be used with equivalent results.b) a one-tailed test should be utilized.c) a two-tailed test should be utilized.d) None of the above.ANSWER:bTYPE: MC DIFFICULTY: Easy KEYWORDS: one-tailed test13. If an economist wishes to determine whether there is evidence that average family income in a community equals $25,000a) either a one-tailed or two-tailed test could be used with equivalent results.b) a one-tailed test should be utilized.c) a two-tailed test should be utilized.d) None of the above.ANSWER:cTYPE: MC DIFFICULTY: Easy KEYWORDS: two-tailed test14. If the p-value is less than in a two-tailed test,a) the null hypothesis should not be rejected.b) the null hypothesis should be rejected.c) a one-tailed test should be used.d) no conclusion should be reached.ANSWER:bTYPE: MC DIFFICULTY: Easy KEYWORDS: p-value, level of significance15. If a test of hypothesis has a Type I error probability () of 0.01, we meana) if the null hypothesis is true, we don't reject it 1% of the time.b) if the null hypothesis is true, we reject it 1% of the time.c) if the null hypothesis is false, we don't reject it 1% of the time.d) if the null hypothesis is false, we reject it 1% of the time.ANSWER:bTYPE: MC DIFFICULTY: Moderate KEYWORDS: type I error, level of significance16. If the Type I error () for a given test is to be decreased, then for a fixed sample size na) the Type II error () will also decrease.b) the Type II error () will increase.c) the power of the test will increase.d) a one-tailed test must be utilized.ANSWER:bTYPE: MC DIFFICULTY: Moderate KEYWORDS: type I error, type II error, sample size17. For a given sample size n, if the level of significance () is decreased, the power of the testa) will increase.b) will decrease.c) will remain the same.d) cannot be determined.ANSWER:bTYPE: MC DIFFICULTY: Moderate KEYWORDS: level of significance, power, sample size18. For a given level of significance (), if the sample size n is increased, the probability of a Type II error () a) will decrease.b) will increase.c) will remain the same.d) cannot be determined.ANSWER:aTYPE: MC DIFFICULTY: Moderate KEYWORDS: level of significance, beta-risk, sample size19. You know that the level of significance () of a test is 5%, you can tell that the probability of committing a Type II error () isa) 2.5%b) 95%.c) 97.5%d) unknownANSWER:dTYPE: MC DIFFICULTY: Moderate KEYWORDS: level of significance, beta-risk20. You know that the probability of committing a Type II error () is 5%, you can tell that the power of the test isa) 2.5%b) 95%.c) 97.5%d) unknownANSWER:bTYPE: MC DIFFICULTY: Easy KEYWORDS: level of significance, beta-risk, power21. If a researcher rejects a true null hypothesis, she has made a _error.ANSWER:Type I TYPE: FI DIFFICULTY: Easy KEYWORDS: type I error22. If a researcher accepts a true null hypothesis, she has made a _decision.ANSWER:correct TYPE: FI DIFFICULTY: Easy KEYWORDS: decision23. If a researcher rejects a false null hypothesis, she has made a _decision.ANSWER:correct TYPE: FI DIFFICULTY: Easy KEYWORDS: decision24. If a researcher accepts a false null hypothesis, she has made a _error.ANSWER:Type II TYPE: FI DIFFICULTY: Easy KEYWORDS: type II error25. It is possible to directly compare the results of a confidence interval estimate to the results obtained by testing a null hypothesis ifa) a two-tailed test for is used.b) a one-tailed test for is used.c) Both of the previous statements are true.d) None of the previous statements is true.ANSWER:aTYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, two-tailed test26. The power of a statistical test isa) the probability of not rejecting H0 when it is false.b) the probability of rejecting H0 when it is true.c) the probability of not rejecting H0 when it is true.d) the probability of rejecting H0 when it is false.ANSWER:dTYPE: MC DIFFICULTY: Moderate KEYWORDS: power27. The symbol for the power of a statistical test isa) .b) 1 .c) .d) 1 .ANSWER:dTYPE: MC DIFFICULTY: Easy KEYWORDS: power28. Suppose we wish to test H0: 47 versus H1: > 47. What will result if we conclude that the mean is greater than 47 when its true value is really 52?a) We have made a Type I error.b) We have made a Type II error.c) We have made a correct decisiond) None of the above are correct.ANSWER:cTYPE: MC DIFFICULTY: ModerateKEYWORDS: one-tailed test, conclusion29. How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: = 52, s = 22. Give the null and alternative hypotheses to determine if the number of tissues used during a cold is less than 60.a)b)c)d)ANSWER:bTYPE: MC DIFFICULTY: ModerateKEYWORDS: one-tailed test, form of hypothesis, form of hypothesis, mean, t test30. How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: = 52, s = 22. Using the sample information provided, calculate the value of the test statistic. a) b)c)d)ANSWER:dTYPE: MC DIFFICULTY: EasyKEYWORDS: one-tailed test, mean, t test31. How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: = 52, s = 22. Suppose the alternative we wanted to test was . State the correct rejection region for = 0.05.a) Reject H0 if t > 1.6604.b) Reject H0 if t < 1.6604.c) Reject H0 if t > 1.9842 or Z < 1.9842.d) Reject H0 if t < 1.9842.ANSWER:bTYPE: MC DIFFICULTY: ModerateKEYWORDS: one-tailed test, mean, t test, rejection region32. How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: = 52, s = 22. Suppose the test statistic does fall in the rejection region at = 0.05. Which of the following decision is correct?a) At = 0.05, we do not reject H0.b) At = 0.05, we reject H0.c) At = 0.05, we accept H0.d) At = 0.10, we do not reject H0.ANSWER:bTYPE: MC DIFFICULTY: EasyKEYWORDS: one-tailed test, mean, t test, decision33. How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: = 52, s = 22. Suppose the test statistic does fall in the rejection region at = 0.05. Which of the following conclusion is correct?a) At = 0.05, there is not sufficient evidence to conclude that the average number of tissues used during a cold is 60 tissues.b) At = 0.05, there is sufficient evidence to conclude that the average number of tissues used during a cold is 60 tissues.c) At = 0.05, there is not sufficient evidence to conclude that the average number of tissues used during a cold is not 60 tissues.d) At = 0.10, there is sufficient evidence to conclude that the average number of tissues used during a cold is not 60 tissues.ANSWER:dTYPE: MC DIFFICULTY: ModerateKEYWORDS: one-tailed test, mean, t test, conclusion34. We have created a 95% confidence interval for with the result (10, 15). What decision will we make if we test at = 0.05?a) Reject H0 in favor of H1.b) Accept H0 in favor of H1.c) Fail to reject H0 in favor of H1.d) We cannot tell what our decision will be from the information given.ANSWER:aTYPE: MC DIFFICULTY: EasyKEYWORDS: two-tailed test, confidence interval, mean, t test, decision35. We have created a 95% confidence interval for with the result (10, 15). What decision will we make if we test at = 0.10?a) Reject H0 in favor of H1.b) Accept H0 in favor of H1.c) Fail to reject H0 in favor of H1.d) We cannot tell what our decision will be from the information given.ANSWER:aTYPE: MC DIFFICULTY: ModerateEXPLANATION: The 90% confidence interval is narrower than (10, 15), which still does not contain 16.KEYWORDS: two-tailed test, confidence interval, mean, t test, decision36. We have created a 95% confidence interval for with the result (10, 15). What decision will we make if we test at = 0.025?a) Reject H0 in favor of H1.b) Accept H0 in favor of H1.c) Fail to reject H0 in favor of H1.d) We cannot tell what our decision will be from the information given.ANSWER:dTYPE: MC DIFFICULTY: ModerateEXPLANATION: The 97.5% confidence interval is wider than (10, 15), which could have contained 16 or not have contained 16.KEYWORDS: two-tailed test, confidence interval, mean, t test, decision37. Suppose we want to test . Which of the following possible sample results based on a sample of size 36 gives the strongest evidence to reject H0 in favor of H1?a) = 28, s = 6b) = 27, s = 4c) = 32, s = 2d) = 26, s = 9ANSWER:bTYPE: MC DIFFICULTY: ModerateKEYWORDS: one-tailed test, rejection region38. Which of the following statements is not true about the level of significance in a hypothesis test?a) The larger the level of significance, the more likely you are to reject the null hypothesis.b) The level of significance is the maximum risk we are willing to accept in making a Type I error.c) The significance level is also called the level.d) The significance level is another name for Type II error.ANSWER:dTYPE: MC DIFFICULTY: ModerateKEYWORDS: level of significance39. If, as a result of a hypothesis test, we reject the null hypothesis when it is false, then we have committeda) a Type II error.b) a Type I error.c) no error.d) an acceptance error.ANSWER:cTYPE: MC DIFFICULTY: ModerateKEYWORDS: decision, type I error, type II error40. The value that separates a rejection region from a non-rejection region is called the _.ANSWER:critical valueTYPE: FI DIFFICULTY: EasyKEYWORDS: critical value, rejection region41. A is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.a) significance levelb) critical valuec) test statisticd) parameterANSWER:cTYPE: MC DIFFICULTY: EasyKEYWORDS: test statistic42. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She woul