Chapter 12

21. For the following information, n = 16 µ = 15 x = 16σ 2 = 16 assume that the population is normal and compute the test statistic if you were testing for a single population mean. (a) z = 1 (b) z = 1 ⁄4 (c) z = 0 (d) z = −1

A

38. If we are trying to establish that the mean of population 1 is greater than the mean of population 2, the appropriate set of hypotheses is (a) H0: µ2 − µ1 ≤0 vs. H1: µ2 − µ1 > 0 (b) H0 : µ1 − µ2 ≥0 vs. H1 : µ1 − µ2 < 0 (c) H0 : µ1 − µ2 = 0 vs. H1 : µ1 − µ2 ≠0 (d) H0: µ1 − µ2 ≤0 vs. H1: µ1 − µ2 > 0

D

15. In testing for the difference of two population means, if the population variances are unknown and the sample sizes from the populations are both greater than or equal to 30, the associated test statistic is approximately a z score.

F

12. If we were testing the hypotheses H0: µ = µ0 vs. H1: µ > µ0 (where µ0 is a specified value of µ) at a given significance level α, with large samples and unknown population variance, then H0 will be rejected if the computed test statistic is (a) z > z α. (b) z < −z α. (c) z > z α/2 . (d) z < −z α/2.

A

2. A right-tailed test is conducted with α = 0.0582. If the z tables are used, the critical value will be (a)−1.57. (b) 1.57. (c)−0.15. (d) 0.15.

B

39. If we are trying to establish that the mean of population 1 is not the same as the mean of population 2, the appropriate set of hypotheses is (a) H0 : µ1 − µ2 ≠0 vs. H1 : µ1 − µ2 = 0. (b) H0: µ1 − µ2 = 0 vs. H1: µ1 − µ2 ≠0. (c) H0: µ1 − µ2 ≥0 vs. H1: µ1 − µ2 < 0. (d) H0: µ1 − µ2 ≤0 vs. H1: µ1 − µ2 > 0.

B

10. The level of significance can be any (a) z value. (b) parameter value. (c) value between 0 and 1, inclusive. (d)αvalue.

C

1. The calculated numerical value that is compared to a table value in a hypothesis test is called the (a) level of significance. (b) critical value. (c) population parameter. (d) test statistic.

D

49. A study was conducted to determine whether remediation in mathematics enabled students to be more successful in college algebra. Success here means that a student received a grade of C or better, and remediation was for one year (students took an equivalent of one year of high school algebra). The following table shows the results of this study. REMEDIAL NONREMEDIAL Sample size n1 = 34 n2 = 150 Number of successes x1 = 20 x2 = 104 If pr and pn are the population proportions for the remedial and nonremedial groups, respectively, the appropriate set of hypotheses for this situation is (a) H0: pr −pn > 0 vs. H0: pr −pn≤0. (b) H0: pr −pn = 0 vs. H0: pr −pn≠0. (c) H0: pr −pn≥0 vs. H0: pr −pn < 0. (d) H0: pr −pn≤0 vs. H0: pr −pn > 0.

D

10. In the P-value approach to hypothesis testing, if 0.01 < P value < 0.05, there is insufficient evidence to reject the null hypothesis.

F

8. If the sample size n is less than 30, then a z score will always be associated with any hypothesis that deals with the mean.

F

9. In the P-value approach to hypothesis testing, if the P value is less than a specified significance level, we fail to reject the null hypothesis.

F

1. A claim or statement about a population parameter is classified as the null hypothesis.

T

20. The local newspaper claims that no more than 5 percent of the residents of the community are on welfare. If you plan to test the claim by taking a random sample from the community, the appropriate set of hypotheses is (a) H0: p≤0.05 vs. H1: p > 0.05. (b) H0: p≥0.05 vs. H1: p < 0.05. (c) H0: p = 0.05 vs. H1: p≠0.05. (d) H0: p > 0.05 vs. H1: p≤0.05.

A

24. For the following information, n = 16 µ = 15 x = 16σ 2 = 16 assume that the population is normal. If you are performing a left-tailed test for a single population mean, then you (a) will reject the null hypothesis if α = 0.2. (b) will not reject the null hypothesis if α = 0.2. (c) will not be able to do the test, since more information is needed. (d) need the hypotheses to be given.

A

26. If a null hypothesis is rejected at the 5 percent significance level for a right-tailed test, you (a) will always reject it at the 0.1 level of significance. (b) will always reject it at the 0.01 level of significance. (c) will always not reject it at the 0.01 level of significance. (d) will sometimes reject it at the 0.06 level of significance.

A

33. For a highly publicized murder trial, it was estimated that 25 percent of the population watched the proceedings on TV. A statistics student felt that this estimate was too small for his community and decided to do a hypothesis test. He selected a random sample of 100 residents from the university community where he lives and found that 32 of them actually watched at least three hours of the proceedings. The computed test statistic for the test is (a) 1.6167. (b) 1.5006. (c)−1.6167. (d)−1.5006.

A

42. Two machines are used to fill 50-lb bags of dog food. Sample information for these two machines is given in the table. The standard deviation (standard error) for the distribution of differences of sample means ( x A−x B) is (a) 0.6205. (b) 0.1931. (c) 0.3850. (d) 0.3217.

A

5. Dr. J claims that 40 percent of his College Algebra class (a very large section) will drop his course by midterm. To test his claim, he selected 45 names at random and discovered that 20 of them had already dropped long before midterm. The test statistic value for his hypothesis test is (a) 0.6086. (b) 0.3704. (c) 8.3333. (d) 0.6847.

A

14. When the P value is used in testing a hypothesis, we will not reject the null hypothesis for a level of significance αwhen (a) P value < α. (b) P value ≥ α. (c) P value = α. (d) P value ≠ α.

B

16. A statistics student was not pleased with his final grade in his statistics course, so he decided to appeal his grade. He believes that the average score on the final examination was less than 69 (out of a possible 100 points), so he believes that it was an unfair examination. He thinks that he should have made at least a grade of B in the course. He decided to test his claim about the average of the final examination. If he knows his "statistics," the correct set of hypothesis he will set up to test his claim is (a) H0: µ ≤69 vs. H1: µ > 69. (b) H0: µ ≥69 vs. H1: µ < 69. (c) H0: µ = 69 vs. H1: µ ≠69. (d) H0: µ ≠69 vs. H1: µ = 69.

B

23. For the following information, n = 16 µ = 15 x = 16σ 2 = 16 assume that the population is normal. If you are performing a right-tailed test for a single population mean, then you (a) will reject the null hypothesis if α = 0.1. (b) will not reject the null hypothesis if α = 0.1. (c) will not be able to do the test, since more information is needed. (d) need the hypotheses to be given.

B

25. If a null hypothesis is rejected at the 0.05 level of significance for a two-tailed test, you (a) will always reject it at the 99 percent level of confidence. (b) will always reject it at the 90 percent level of confidence. (c) will always not reject it at the 99 percent level of confidence. (d) will always not reject it at the 96 percent level of confidence.

B

28. It was reported that a certain population had a mean of 27. To test this claim, you selected a random sample of size 100. The computed sample mean and sample standard deviation were 25 and 7, respectively. The appropriate set of hypotheses for this test is (a) H0: µ ≤27 vs. H1: µ > 27. (b) H0: µ = 27 vs. H1: µ ≠27. (c) H0 : µ ≥25 vs. H1 : µ < 25. (d) H0: µ ≠25 vs. H1: µ = 25.

B

34. For a highly publicized murder trial, it was estimated that 25 percent of the population watched the proceedings on TV. A statistics student felt that this estimate was too small for his community and decided to do a hypothesis test. He selected a random sample of 100 residents from the university community where he lives and found that 32 of them actually watched at least three hours of the proceedings. The P value for the test is (a) 0.4332. (b) 0.0526. (c) 0.0668. (d) 0.4474.

B

41. Two machines are used to fill 50-lb bags of dog food. Sample information for these two machines is given in the table. x1 + x2 n1 −n2 The point estimate for the difference between the two population means (µ A− µ B) is (a) 17. (b) 3. (c) 4. (d)−4.

B

45. Two machines are used to fill 50-lb bags of dog food. Sample information for these two machines is given in the table. MACHINE A MACHINE B Sample size 81 64 Sample mean (pounds) 51 48 Sample variance 16 12 MACHINE A MACHINE B Sample size 81 64 Sample mean (pounds) 51 48 Sample variance 16 12 If you are to conduct a test to determine whether the average amount dispensed by machine A is significantly more than the average amount dispensed by machine B, the P value for the test is (a) approximately 0.5. (b) approximately 0.0. (c) approximately 1.0. (d) none of the above answers.

B

46. Two machines are used to fill 50-lb bags of dog food. Sample information for these two machines is given in the table. REMEDIAL NONREMEDIAL Sample size n1 = 34 n2 = 150 Number of successes x1 = 20 x2 = 104 If we assume that the two population proportions are both equal to p, then a point estimate for p is (a) 0.4565. (b) 0.6739. (c) 0.4078. (d) 0.7241. If you are to conduct a test at the 0.01 significance level to determine whether the average amount dispensed by machine A is significantly more than the average amount dispensed by machine B, the correct decision is (a) do not reject the null hypothesis. (b) reject the null hypothesis. (c) reject the alternative hypothesis. (d) do not reject the alternative hypothesis.

B

47. A study was conducted to determine whether remediation in mathematics enabled students to be more successful in college algebra. Success here means that a student received a grade of C or better, and remediation was for one year (students took an equivalent of one year of high school algebra). The following table shows the results of this study. If we assume that the two population proportions are both equal to p, then a point estimate for p is (a) 0.4565. (b) 0.6739. (c) 0.4078. (d) 0.7241.

B

50. A study was conducted to determine whether remediation in mathematics enabled students to be more successful in college algebra. Success here means that a student received a grade of C or better, and remediation was for one year (students took an equivalent of one year of high school algebra). The following Table shows the results of this study Remedial Nonremedial Sample Size N1=34 N2=150 Number of successes X1=20 X2=104 If Pr and Pn are the population proportions for the remedial and nonremedial goups respectively, the computed test statistic for the appropriate test is (a) 3.6426 (b) -1.1803 (c) -13.2685 (d) 1.3931

B

6. In testing a hypothesis, the hypothesis that is assumed to be true is (a) the alternative hypothesis. (b) the null hypothesis. (c) the null or the alternative hypothesis. (d) neither the null nor the alternative hypothesis.

B

8. A Type II error is defined to be the probability of (a) failing to reject a true null hypothesis. (b) failing to reject a false null hypothesis. (c) rejecting a false null hypothesis. (d) rejecting a true null hypothesis.

B

17. An advertisement on the TV claims that a certain brand of tire has an average lifetime of 50,000 miles. Suppose you plan to test this claim by taking a sample of tires and putting them on test. The correct set of hypotheses to set up is (a) H0: µ ≤50,000 vs. H1: µ > 50,000. (b) H0 : µ ≥50,000 vs. H1 : µ < 50,000. (c) H0: µ = 50,000 vs. H1: µ ≠50,000. (d) H0: µ ≠50,000 vs. H1: µ = 50,000.

C

19. The local newspaper claims that 15 percent of the residents of the community play the state lottery. If you plan to test the claim by taking a random sample from the community, the appropriate set of hypotheses is (a) H0: p≥0.15 vs. H1: p < 0.15. (b) H0: p≤0.15 vs. H1: p > 0.15. (c) H0 : p = 0.15 vs. H1 : p≠0.15. (d) H0: p≠0.15 vs. H1: p = 0.15.

C

22. For the following information n = 16 µ = 15 x = 16σ 2 = 16 assume that the population is normal. If you are performing a right-tailed test for a single population mean, then (a) P value = 0.3413. (b) P value < 0.05. (c) P value = 0.1587. (d) P value = 0.0794.

C

27. For a left-tailed test concerning the population proportion with sample size 203 and α = 0.05, the null hypothesis will be rejected if the computed test statistic is (a) less than −1.96. (b) less than −1.717. (c) less than −1.645. (d) less than −2.704.

C

3. A right-tailed test is performed, with the test statistic having a standard normal distribution. If the computed test statistic is 3.00, the P value for this test is (a) 0.4996. (b) 0.9996. (c) 0.0013. (d) 0.0500.

C

30. It was reported that a certain population had a mean of 27. To test this claim, you selected a random sample of size 100. The computed sample mean and sample standard deviation were 25 and 7, respectively. The P value for the appropriate set of hypotheses is (a) 0.0021. (b) 0.9979. (c) 0.0042. (d)−0.4979.

C

31. It was reported that a certain population had a mean of 27. To test this claim, you selected a random sample of size 100. The computed sample mean and sample standard deviation were 25 and 7, respectively. At the 0.05 level of significance, you can claim that the average of this population is (a) not equal to 25. (b) equal to 25. (c) not equal to 27. (d) equal to 27.

C

36. For a highly publicized murder trial, it was estimated that 25 percent of the population watched the proceedings on TV. A statistics student felt that this estimate was too small for his community and decided to do a hypothesis test. He selected a random sample of 100 residents from the university community where he lives and found that 32 of them actually watched at least three hours of the proceedings. The standard deviation for the distribution of the sample proportion is (a) 0.19. (b) 4.67. (c) 4.33. (d) 0.23.

C

37. IF two large samples are selected independently from two different populations, the sampling distribution of the difference of the sample means (a) has a mean that is the sum of the two populations (b) has a variance that is the sum of the two population means (c) has a distribution that is approximately normal (d) has a mean and variance that are the average of the two population means and variances, respectively.

C

40. In performing hypothesis tests for the difference of two population proportions, if n1 and n2 are the respective sample sizes and x1 and x2 are the respective successes, then the pooled estimate of the difference of the population proportions is given by (a) . (b) . (c) . (d) .

C

44. Two machines are used to fill 50-lb bags of dog food. Sample information for these two machines is given in the table. MACHINE A MACHINE B Sample size 81 64 Sample mean (pounds) 51 48 Sample variance 16 12 If you are to conduct a test to determine whether the average amount dispensed by machine A is significantly more than the average amount dispensed by machine B, the computed test statistic for this test is (a) 7.7918. (b)−7.7918. (c) 4.8348. (d) 2.1988.

C

11. If you fail to reject the null hypothesis in the testing of a hypothesis, then (a) a Type I error has definitely occurred. (b) a Type II error has definitely occurred. (c) the computed test statistic is incorrect. (d) there is insufficient evidence to claim that the alternative hypothesis is true.

D

13. Which of the following general guidelines is used when using the P value to perform hypothesis tests? (a) If the P value > 0.1, there is little or no evidence to reject the null hypothesis. (b) If 0.01 < P value ≤0.05, there is moderate evidence to reject the null hypothesis. (c) If the P value ≤0.001, there is very strong evidence to reject the null hypothesis. (d) All of the above.

D

15. A real estate agent claims that the average price for homes in a certain subdivision is $150,000. You believe that the average price is lower. If you plan to test his claim by taking a random sample of the prices of the homes in the subdivision, the formulated set of hypotheses will be (a) H0: µ ≤150,000 vs. H1: µ > 150,000. (b) H0: µ = 150,000 vs. H1: µ ≠150,000. (c) H0: µ < 150,000 vs. H1: µ ≥150,000. (d) H0 : µ ≥150,000 vs. H1 : µ < 150,000.

D

18. The local newspaper reported that at least 25 percent of the population in a university community works at the university. You believe that the proportion is lower. If you selected a random sample to test this claim, the appropriate set of hypotheses would be (a) H0: p≤0.25 vs. H1: p > 0.25. (b) H0: p = 0.25 vs. H1: p≠0.25. (c) H0: p < 0.25 vs. H1: p≥0.25. (d) H0 : p≥0.25 vs. H1 : p < 0.25.

D

29. It was reported that a certain population had a mean of 27. To test this claim, you selected a random sample of size 100. The computed sample mean and sample standard deviation were 25 and 7, respectively. The computed test statistic for the appropriate set of hypotheses is (a)−4.0816. (b)−0.4082. (c)−28.5714. (d)−2.8571.

D

32. For a highly publicized murder trial, it was estimated that 25 percent of the population watched the proceedings on TV. A statistics student felt that this estimate was too small for his community and decided to do a hypothesis test. He selected a random sample of 100 residents from the university community where he lives and found that 32 of them actually watched at least three hours of the proceedings. The appropriate set of hypotheses for the test is (a) H0 : p≤0.32 vs. H1 : p > 0.32. (b) H0: p≥0.25 vs. H1: p < 0.25. (c) H0: p≥0.32 vs. H1: p < 0.32. (d) H0: p≤0.25 vs. H1: p > 0.25.

D

35. For a highly publicized murder trial, it was estimated that 25 percent of the population watched the proceedings on TV. A statistics student felt that this estimate was too small for his community and decided to do a hypothesis test. He selected a random sample of 100 residents from the university community where he lives and found that 32 of them actually watched at least three hours of the proceedings. At the 10 percent significance level, you can claim that the proportion of viewers in this community was (a) significantly greater than 32 percent. (b) significantly smaller than 32 percent. (c) significantly smaller than 25 percent. (d) significantly greater than 25 percent.

D

43. Two machines are used to fill 50-lb bags of dog food. Sample information for these two machines is given in the table. MACHINE A MACHINE B Sample size 81 64 Sample mean (pounds) 51 48 Sample variance 16 12 MACHINE A MACHINE B Sample size 81 64 Sample mean (pounds) 51 48 Sample variance 16 12 If you are to conduct a test to determine whether the average amount dispensed by machine A is significantly more than the average amount dispensed by machine B, the appropriate set of hypotheses is (a) H0 : µ B− µ A≤0 vs. H1 : µ B− µ A > 0. (b) H0 : µ A− µ B = 0 vs. H1 : µ A− µ B≠0. (c) H0: µ A− µ B≥0 vs. H1: µ A− µ B < 0. (d) H0 : µ A− µ B≤0 vs. H1 : µ A− µ B > 0.

D

48. A study was conducted to determine whether remediation in mathematics enabled students to be more successful in college algebra. Success here means that a student received a grade of C or better, and remediation was for one year (students took an equivalent of one year of high school algebra). The following table shows the results of this study. REMEDIAL NONREMEDIAL Sample size n1 = 34 n2 = 150 Number of successes x1 = 20 x2 = 104 If we assume that the two population proportions are both equal to p, then an estimate for the standard deviation for the distribution of differences of sample proportions is approximately (a) 0.0079. (b) 0.1898. (c) 0.0360. (d) 0.0890.

D

7. A Type I error is defined to be the probability of (a) failing to reject a true null hypothesis. (b) failing to reject a false null hypothesis. (c) rejecting a false null hypothesis. (d) rejecting a true null hypothesis.

D

9. In hypothesis testing, the level of significance is the probability of (a) failing to reject a true null hypothesis. (b) failing to reject a false null hypothesis. (c) rejecting a false null hypothesis. (d) rejecting a true null hypothesis.

D

16. In making inferences on the difference of two population proportions, the calculated (pooled) proportion is given by p ˆ= , where x1 and x2 are the respective numbers of successes from populations 1 and 2, and n1 and n2 are the respective sample sizes.

F

17. If the null hypothesis is rejected, this means that the null hypothesis is not true.

F

19. The P value of a hypothesis test can be computed without the value of the test statistic.

F

21. In hypothesis testing, the alternative hypothesis is assumed to be true.

F

22. In hypothesis testing, if the null hypothesis is rejected, the alternative hypothesis must also be rejected.

F

3. If we want to claim that a population parameter is different from a specified value, this situation can be considered as a one-tailed test.

F

4. New software is being integrated into the teaching of a course with the hope that it will help to improve the overall average score for this course. The historical average score for this course is 72. If a statistical test is done for this situation, the alternative hypothesis will be (a) H1: µ ≠72. (b) H1: µ < 72. (c) H1 : µ = 72. (d) H1: µ > 72.

F

5. A Type I error is the error we make when we fail to reject an incorrect null hypothesis.

F

11. In the P-value approach to hypothesis testing, if P value < 0.001, there is very strong evidence to reject the null hypothesis.

T

12. When large samples (n≥30) are associated with hypothesis tests for population proportions, the associated test statistic is a z score.

T

13. The distribution of sample proportions from a single population is approximately normal provided that the sample size is large enough (n≥30).

T

14. The distribution of the difference between two sample means is approximately normal with variance + , where n1 and n2 are the sample sizes from populations 1 and 2, respectively, and σ1 2 and σ2 2 are the respective variances, if the sample sizes are both greater than or equal to 30.

T

18. When performing hypothesis tests on two population means, it is necessary to assume that the populations are normally distributed.

T

2. A statement contradicting the claim in the null hypothesis about a population parameter is classified as the alternative hypothesis.

T

20. The P value of a hypothesis test is the smallest level of significance at which the null hypothesis can be rejected.

T

4. The null hypothesis is considered correct until proven otherwise.

T

6. The probability of making a Type I error and the level of significance are equal or the same.

T

7. The range of z values that indicates that there is a significant difference between the value of the sample statistic and the proposed parameter value is called the rejection region or the critical region.

T