## Business Statistics in Practice 3rd Canadian Edition By Bruce – Test Bank

c7 Student: ___________________________________________________________________________ 1. The further the hypothesized mean is from the actual mean, the greater the power of the test. True False The manager of the quality department for a tire manufacturing company wants to know the average tensile strength of rubber used in making a certain brand of radial tire. The population is normally distributed and the population standard deviation is known. The manager uses a z test to test the null hypothesis that the mean tensile strength is less than or equal to 800. The calculated z test statistic is a positive value that leads to a p-value of .067 for the test. 2. If the significance level is .10, the null hypothesis would be rejected. True False 3. If the significance level is .05, the null hypothesis would be rejected. True False The manager of the quality department for a tire manufacturing company wants to know the average tensile strength of rubber used in making a certain brand of radial tire. The population is normally distributed and the population standard deviation is known. The manager uses a z test to test the null hypothesis that the mean tensile strength is 800. The calculated z test statistic is a positive value that leads to a p-value of .045 for the test. 4. If the significance level is .01, the null hypothesis would be rejected. True False 5. If the significance level is .05, the null hypothesis would be rejected. True False 6. A Type I error is rejecting a true null hypothesis. True False 7. The larger the p-value, the more we doubt the null hypothesis. True False 8. A Type II error is failing to reject a false null hypothesis. True False 9. You cannot make a Type II error when the null hypothesis is true. True False 10. For a hypothesis test about a population mean, if the level of significance is less than the p-value, the null hypothesis is rejected. True False 11. The significance level, , is the probability that the test statistic would assume a value as or more extreme than the observed value of the test statistic. True False 12. Everything else being constant, increasing the sample size decreases the probability of committing a Type II error. True False 13. The null hypothesis is a statement that will be accepted only if there is convincing sample evidence that it is true. True False 14. The power of a statistical test is the probability of rejecting the null hypothesis when it is true. True False 15. As the level of significance increases, we are more likely to reject the null hypothesis. True False 16. In hypothesis testing, a test statistic is computed from sample data and is used in making a decision about whether or not to reject the null hypothesis. True False 17. When conducting a hypothesis test about a population mean, other relevant factors held constant, increasing the level of significance from .05 to .10 will reduce the probability of a Type I error. True False 18. When conducting a hypothesis test about a population mean, other relevant factors held constant, increasing the level of significance from .05 to .10 will reduce the probability of a Type II error. True False 19. The level of significance indicates the probability of rejecting a false null hypothesis. True False 20. When conducting a hypothesis test about a population mean, reducing the level of significance will increase the size of the rejection region. True False 21. When the null hypothesis is not rejected, there is no possibility of making a Type I error. True False 22. When the null hypothesis is true, there is no possibility of making a Type I error. True False 23. When testing for a difference between two population proportions based on large, independent samples, the test statistic used is based on the z distribution. True False 24. In testing the difference between the means of two normally distributed populations with known population standard deviations, the samples we take from each population must be independent. True False 25. In testing the difference between the means of two normally distributed populations with known population standard deviations, the two sample sizes must be equal. True False 26. In testing the difference between the means of two normally distributed populations with known population standard deviations, the alternative hypothesis indicates no differences between the two specified means. True False 27. In testing the difference between the means of two normally distributed populations with known population standard deviations, we can only use a two-sided test. True False 28. Consider testing the difference between the means of two populations with known population standard deviations. If neither population is normally distributed, then the sampling distribution of the difference in sample means will still be approximately normal provided that the sample sizes are sufficiently large and the samples are independent. True False 29. When we are testing a hypothesis about the difference in two population proportions based on large, independent samples, we compute a combined (pooled) proportion from the two samples if we assume that there is no difference between the two proportions in our null hypothesis. True False 30. Which statement is incorrect? A. The null hypothesis contains the equality sign. B. When a false null hypothesis is not rejected, a Type II error has occurred. C. We reject the null hypothesis whenever the p-value is less than the significance level. D. Rejecting the null hypothesis when it should not be rejected is a Type I error. E. If we fail to reject the null hypothesis, then it is proven that null hypothesis is true. 31. For a given hypothesis test, if we do not reject H0 when H0 is true then which one of the following statements is true? A. No error has been committed. B. Type I error has been committed. C. Type II error has been committed. D. The power of the test has increased. E. The power of the test has decreased. 32. If a null hypothesis is rejected at a significance level of 0.01, it will ______ be rejected at a significance level of _____. A. always, 0.05 B. never, 0.05 C. always, 0.01 D. never, 0.01 E. never, 0.10 33. If a null hypothesis is rejected at a significance level of 0.05, it will ______ be rejected at a significance level of _____. A. always, 0.01 B. sometimes, 0.01 C. never, 0.01 D. never, 0.10 E. sometimes, 0.10 34. If a null hypothesis is NOT rejected at a significance level of 0.05, it will ______ be rejected at a significance level of _____. A. always, 0.10 B. sometimes, 0.01 C. never, 0.01 D. never, 0.10 E. always, 0.01 35. When testing a hypothesis about a population proportion, if np0 5 and n(1 – p0) 5, then the test statistics is based on the ___ distribution. A. z B. t C. F D. chi-square E. exponential 36. If the null hypothesis in a one-sided hypothesis test for a population mean is rejected at the 5% level of significance, then the null hypothesis in the corresponding hypothesis two-sided test is guaranteed to be rejected at the ____ level of significance. A. 10% B. 5% C. 2.5% D. 1% E. 0.1% 37. If the null hypothesis in a two-sided hypothesis test for a population mean cannot be rejected at the 10% level of significance, then it is still possible that the null hypothesis in the corresponding one-sided hypothesis test could be rejected at the ____ level of significance. A. 10% B. 5% C. 2.5% D. 1% E. 0.1% 38. If a one-sided hypothesis test for a population mean yields a p-value of 0.041, then what is the smallest level of significance at which the null hypothesis in the corresponding two-sided hypothesis test can be rejected? A. 10% B. 5% C. 2.5% D. 1% E. 0.1% 39. If a one-sided hypothesis test for a population mean yields a p-value of 0.023, then what is the smallest level of significance at which the null hypothesis in the corresponding two-sided hypothesis test can be rejected? A. 10% B. 5% C. 2.5% D. 1% E. 0.1% 40. A Type II error occurs if we _________ H0 when it should ___________. A. fail to reject; be rejected B. fail to reject; not be rejected C. reject, not be rejected D. reject, rejected E. reject, accepted 41. A professional basketball player is averaging 21 points per game. He will be retiring at the end of this season. The team has multiple options to replace him. However, the owner feels that signing a replacement is only justified, if he can average more than 22 points per game. Which of the following are the appropriate hypotheses for this problem? A. H0: 21 vs. Ha: > 21 B. H0: 22 vs. Ha: > 22 C. H0: 21 vs. Ha: < 21 D. H0: 22 vs. Ha: < 22 E. H0: 22 vs. Ha: = 22 42. A decision in a hypothesis test can be made by using _____. A. a p-value. B. a critical value. C. the sample size. D. either a p-value or a critical value. E. either a critical value or the sample size. 43. The smaller the _____, the stronger the evidence is against the null hypothesis. A. Type II error B. Type I error C. rejection point D. p-value E. sample size 44. When carrying out a test of H0: = 10 vs. Ha: > 10 by using a critical value, we reject H0 at level of significance when the calculated test statistic is: A. Less than B. Less than – C. Greater than D. Greater than E. Less than the p-value 45. When carrying out a test of H0: p = .4 versus Ha: p < .4 and z is the calculated test statistic, we reject H0 at level of significance when: A. z < – B. z < – C. z > D. p-value > E. p-value > 2 46. When carrying out a test of H0: = 10 vs. Ha: 10 by using a p-value, we reject H0 at level of significance alpha when the p-value is: A. Greater than /2 B. Greater than C. Less than D. Less than /2 E. Less than 47. If a two-sided hypothesis test for a population mean yields a p-value of 0.0651, then what is the smallest level of significance at which the null hypothesis in a corresponding one-sided hypothesis test can be rejected? A. 10% B. 5% C. 2.5% D. 1% E. 0.1% 48. In a two-sided hypothesis test, if the p-value is less than , then A. H0 is rejected. B. H0 is not rejected. C. H0 may or may not be rejected depending on the sample size n. D. additional information is needed to make a decision about H0. E. Ha is rejected 49. When conducting a hypothesis test about a population mean at a given level of significance, as the sample size n increases the power of the test _____. A. decreases B. increases C. may increase or decrease D. remains the same E. will converge to the probability of a Type II error. 50. When conducting a hypothesis test about a population mean at a given level of significance, as the sample size n increases the probability of a Type II error: A. decreases. B. increases. C. may increase or decrease. D. remains the same. E. will converge to the probability of a Type I error. 51. For the following hypothesis test where H0: 10 vs. Ha: > 10, we reject H0 at level of significance and conclude that the true mean is greater than 10 when the true mean is really 8. Based on this information we can state that we have: A. Made a Type I error B. Made a Type II error C. Made a correct decision D. Increased the power of the test E. Decreased the power of the test 52. For the following hypothesis test where H0: 10 vs. Ha: > 10, we reject H0 at level of significance and conclude that the true mean is greater than 10 when the true mean is really 14. Based on this information we can state that we have: A. Made a Type I error B. Made a Type II error C. Made a correct decision D. Increased the power of the test E. Decreased the power of the test 53. The power of a statistical test is the probability of ______________ the null hypothesis when it is ________. A. not rejecting, false B. not rejecting, true C. rejecting, false D. rejecting, true E. accepting, false 54. A researcher suspects that the unemployment rate in her province is greater than 8%. What is the appropriate alternative hypothesis? A. Ha: p 0.08 B. Ha: p = 0.08 C. Ha: p 0.08 D. Ha: p < 0.08 E. Ha: p > 0.08 55. Suppose that you are conducting a hypothesis test about a population mean. Holding all other relevant factors constant, which of the following actions will result in an increase in the size of the rejection region? A. Increase the sample size. B. Decrease the sample size. C. Increase the sample size and decrease the level of significance. D. Decrease the sample size and increase the level of significance. E. Increase the level of significance. 56. The average customer waiting time at a fast food restaurant has been 7.5 minutes. The customer waiting time has a normal distribution. The manager claims that the use of a new system will decrease average customer waiting time. What is the null and alternative hypothesis for this scenario? A. H0: = 7.5 and Ha 7.5 B. H0: 7.5 and Ha > 7.5 C. H0: 7.5 and Ha < 7.5 D. H0: > 7.5 and Ha 7.5 E. H0: > 7.5 and Ha 7.5 A major airline company is concerned that its proportion of late arrivals has substantially increased in the past month. Historical data shows that on the average 18% of the company airplanes have arrived late. In a random sample of 1,240 airplanes, 310 airplanes have arrived late. If we are conducting a hypothesis test of a single proportion to determine if the proportion of late arrivals has increased: 57. What is the correct statement of null and alternative hypothesis? A. H0: p < .18 and HA: p .18 B. H0: p .18 and HA: p > .18 C. H0: p = .18 and HA: p .18 D. H0: p > .18 and HA: p .18 E. H0: p .20 and HA: p > .20 58. What is the value of the calculated test statistic? A. z = 6.416 B. z = 3.208 C. z = -3.208 D. z = -6.416 E. z = 1.833 A company has developed a new ink-jet cartridge for its printer that it believes has a longer life-time on average than the one currently being produced. To investigate its length of life, 225 of the new cartridges were tested by counting the number of high-quality printed pages each was able to produce. The sample mean was determined to be 1511.4 pages. The population standard deviation is known to be 35.7 pages. The historical average lifetime for cartridges produced by the current process is 1502.5 pages. 59. The null and alternative hypotheses to test whether the mean lifetime of the new cartridges exceeds that of the old cartridges is _____. A. HO: = 1502.5 vs. HA: 1502.5 B. HO: 1511.4 vs. HA: < 1511.4 C. HO: 1502.5 vs. HA: < 1502.5 D. HO: 1502.5 vs. HA: = 1502.5 E. HO: 1502.5 vs. HA: > 1502.5 60. The appropriate test statistic to test the hypotheses is _____. A. 56.09 B. 3.74 C. 22.34 D. -3.74 E. -22.34 61. What is the rejection point for = .05 to test the hypotheses? A. 1.645 B. -1.645 C. 1.96 D. 1.28 E. -1.96 62. How much evidence do we have that the new cartridge is better than the old? A. No evidence B. Some evidence C. Strong evidence D. Very strong evidence E. Extremely strong evidence In a study of distances traveled by buses before the first major engine failure, a sample of 191 buses results in a mean of 96,700 km. The population standard deviation is known to be 37,500 km. 63. The null and alternative hypotheses to test the claim that the mean distance traveled before a major engine failure is more than 90,000 km is _____. A. HO: = 90,000 vs. HA: 90,000 B. HO: 90,000 vs. HA: < 90,000 C. HO: 96,700 vs. HA: < 96,700 D. HO: 90,000 vs. HA: = 90,000 E. HO: 90,000 vs. HA: > 90,000 64. The appropriate test statistic to test the hypotheses is _____. A. 2.47 B. 34.13 C. 478.16 D. -34.13 E. -2.47 65. The p-value corresponding to the test statistic is _____. A. 0.0000 B. 0.0068 C. -0.0068 D. 0.0136 E. -0.0136 66. How much evidence is there that the major engine failure will occur after 90,000 km? A. No evidence B. Some evidence C. Strong evidence D. Very strong evidence E. Extremely strong evidence A psychologist has designed a new intelligence test. Historically, time to complete the old test was an average of 120 minutes. With the altered format of the test, the psychologist claims that the time to complete the test is no longer 120 minutes. A sample of 50 new test taking times yielded an average time of 118 minutes. The population standard deviation is known to be 5 minutes. 67. The null and alternative hypothesis to test if the average time to complete the test had changed from 120 minutes is _____. A. H0: µ = 120 Ha: µ 120 B. H0: µ 120 Ha: µ < 120 C. H0: µ 120 Ha: µ > 120 D. H0: µ 120 Ha: µ = 120 E. H0: µ 118 Ha: µ < 118 68. The test statistic to test these hypotheses is _____. A. -2.83 B. -6.32 C. 5.64 D. -5.64 E. 2.82 69. The p-value is _____. A. .0024 B. -.0024 C. .0000 D. -.0048 E. .0046 70. How much evidence do we have to reject the null hypothesis? A. No evidence B. Some evidence C. Strong evidence D. Very Strong evidence E. Extremely Strong evidence The manager of a grocery store wants to determine whether the amount of water contained in a 1L bottle purchased from a known manufacturer actually averages to 1L. It is known from the manufacturer’s specifications that the standard deviation of the amount of water is equal to 0.02L. A random sample of 32 bottles is selected, and the mean amount of water per 1L bottle is found to be 0.995L. 71. The null and alternative hypotheses to test that the manufacturer’s claim is false is _____. A. H0: µ .995 Ha: µ > .995 B. H0: µ 1 Ha: µ = 1 C. H0: µ 1 Ha: µ < 1 D. H0: µ = 1 Ha: µ 1 E. H0: µ 1 Ha: µ > 1 72. The test statistic is _____. A. -2.83 B. -1.41 C. -2.00 D. 2.83 E. 1.41 73. The p-value is _____. A. .0793 B. .1586 C. .0023 D. .0046 E. .0456 74. How much evidence do we have that the manufacturer’s claim is false? A. No evidence B. Some evidence C. Strong evidence D. Very Strong evidence E. Extremely Strong evidence The quality control manager at a cell phone battery factory needs to determine whether the mean life of a large shipment of batteries is equal to the specified value of 375 hours. The process standard deviation is known to be 100 hours. A random sample of 64 batteries indicates a sample mean of 350 hours.

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