Statistical Inferences about Two Populations Exam Prep Ch10

CHAPTER 10

STATISTICAL INFERENCES ABOUT TWO POPULATIONS

CHAPTER LEARNING OBJECTIVES

1. Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic. The population means are analyzed by comparing two sample means. When sample sizes are large (n ≥ 30) and population variances are known, a z test is used. When sample sizes are small, the population variances are known, and the populations are normally distributed, the z test is used to analyze the population means. If the population variances are unknown, and the populations are normally distributed, the t test of means for independent samples is used. For populations that are related on some measure, such as twins or before-and-after, a t test for dependent measures (matched pairs) is used. The difference in two population proportions can be tested or estimated using a z test.

2. Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test. The population means are analyzed by comparing two sample means. When sample sizes are large (n ≥ 30) and population variances are known, a z test is used. When sample sizes are small, the population variances are known, and the populations are normally distributed, the z test is used to analyze the population means. If the population variances are unknown, and the populations are normally distributed, the t test of means for independent samples is used. For populations that are related on some measure, such as twins or before-and-after, a t test for dependent measures (matched pairs) is used. The difference in two population proportions can be tested or estimated using a z test.

3. Test hypotheses and develop confidence intervals about the difference in two dependent populations. The population means are analyzed by comparing two sample means. When sample sizes are large (n ≥ 30) and population variances are known, a z test is used. When sample sizes are small, the population variances are known, and the populations are normally distributed, the z test is used to analyze the population means. If the population variances are unknown, and the populations are normally distributed, the t test of means for independent samples is used. For populations that are related on some measure, such as twins or before-and-after, a t test for dependent measures (matched pairs) is used. The difference in two population proportions can be tested or estimated using a z test.

4. Test hypotheses and develop confidence intervals about the difference in two population proportions. The population means are analyzed by comparing two sample means. When sample sizes are large (n ≥ 30) and population variances are known, a z test is used. When sample sizes are small, the population variances are known, and the populations are normally distributed, the z test is used to analyze the population means. If the population variances are unknown, and the populations are normally distributed, the t test of means for independent samples is used. For populations that are related on some measure, such as twins or before-and-after, a t test for dependent measures (matched pairs) is used. The difference in two population proportions can be tested or estimated using a z test.

5.Test hypotheses about the difference in two population variances using the F distribution. The population variances are analyzed by an F test when the assumption that the populations are normally distributed is met. The F value is a ratio of the two variances. The F distribution is a distribution of possible ratios of two sample variances taken from one population or from two populations containing the same variance.

TRUE-FALSE STATEMENTS

1. To determine if there is a difference in the strength of steel produced from two different production processes, a process manager will draw independent samples from the two processes and compare the difference in the sample means.

Difficulty: Easy

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.

Section Reference: 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)

Bloom’s: Application

AACSB: Reflective Thinking

2. The difference in two sample means is normally distributed for sample sizes ≥ 30, only if the populations are normally distributed.

Difficulty: Easy

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.

Section Reference: 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)

Bloom’s: Knowledge

AACSB: Reflective Thinking

3. If the sample sizes are greater than 30 and the population variances are known, the basis for statistical inferences about the difference in two population means using two independent random samples is the z statistic, regardless of the shapes of the population distributions.

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.

Section Reference: 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)

Bloom’s: Knowledge

AACSB: Reflective Thinking

4. If the sample sizes are small, but the populations are normally distributed and the population variances are known, the z statistic can be used as the basis for statistical inferences about the difference in two population means using two independent random samples.

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.

Section Reference: 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)

Bloom’s: Knowledge

AACSB: Reflective Thinking

5. If a 98% confidence interval for the difference in the two population means does not contain zero, then the null hypothesis of zero difference between the two population means cannot be rejected at a 0.02 level of significance.

Difficulty: Hard

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.

Section Reference: 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)

Bloom’s: Analysis

AACSB: Reflective Thinking

6. If a 90% confidence interval for the difference in the two population means contains zero, then the null hypothesis of zero difference between the two population means cannot be rejected at a 0.10 level of significance.

Difficulty: Hard

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.

Section Reference: 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)

Bloom’s: Analysis

AACSB: Reflective Thinking

7. If the populations are normally distributed but the population variances are unknown, the z statistic can be used as the basis for statistical inferences about the difference in two population means using two independent random samples.

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.

Bloom’s: Knowledge

AACSB: Reflective Thinking

8. If the populations are normally distributed but the population variances are unknown, the t statistic can be used as the basis for statistical inferences about the difference in two population means using two independent random samples.

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.

Bloom’s: Knowledge

AACSB: Reflective Thinking

9. If the variances of the two populations are not equal, it is appropriate to use the “pooled” formula to determine the t statistic for the hypothesis test of the difference in the two population means.

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.

Bloom’s: Comprehension

AACSB: Reflective Thinking

10. If the variances of the two populations are equal, it is appropriate to use the “pooled” formula to determine the t statistic for the hypothesis test of the difference in the two population means.

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.

Bloom’s: Comprehension

AACSB: Reflective Thinking

11. If the variances of the two populations are not equal, it is appropriate to use the “unpooled” formula to determine the t statistic for the hypothesis test of the difference in the two population means.

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.

Bloom’s: Comprehension

AACSB: Reflective Thinking

12. In order to construct an interval estimate for the difference in the means of two normally distributed populations with unknown but equal variances, using two independent samples of size n₁ and n₂, we must use a t distribution with (n₁ + n₂) degrees of freedom.

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.

Bloom’s: Knowledge

AACSB: Reflective Thinking

13. In order to construct an interval estimate for the difference in the means of two normally distributed populations with unknown but equal variances, using two independent samples of size n₁ and n₂, we must use a t distribution with (n₁ + n₂ − 2) degrees of freedom.

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.

Bloom’s: Knowledge

AACSB: Reflective Thinking

14. In a set of matched samples, each data value in one sample is related to or matched with a corresponding data value in the other sample.

Difficulty: Easy

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two dependent populations.

Section Reference: 10.3 Statistical Inferences for Two Related Populations

Bloom’s: Knowledge

AACSB: Reflective Thinking

15. Sets of matched samples are also referred to as independent samples.

Difficulty: Easy

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two dependent populations.

Section Reference: 10.3 Statistical Inferences for Two Related Populations

Bloom’s: Knowledge

AACSB: Reflective Thinking

16. Sets of matched samples are also referred to as dependent samples.

Difficulty: Easy

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two dependent populations.

Section Reference: 10.3 Statistical Inferences for Two Related Populations

Bloom’s: Knowledge

AACSB: Reflective Thinking

17. To test hypotheses about the equality of two population variances, the ratio of the variances of the samples from the two populations is tested using the F test.

Difficulty: Medium

Learning Objective: Test hypotheses about the difference in two population variances using the F distribution.

Section Reference: 10.5 Testing Hypotheses about Two Population Variances

Bloom’s: Knowledge

AACSB: Reflective Thinking

18. The F test of two population variances is extremely robust to the violations of the assumption that the populations are normally distributed.

Difficulty: Medium

Learning Objective: Test hypotheses about the difference in two population variances using the F distribution.

Section Reference: 10.5 Testing Hypotheses about Two Population Variances

Bloom’s: Comprehension

AACSB: Reflective Thinking

MULTIPLE CHOICE QUESTIONS

19. Restaurateur Denny Valentine is evaluating two sites, Raymondville and Rosenberg, for his next restaurant. He wants to prove that Raymondville residents (population 1) dine out more often than Rosenberg residents (population 2). Denny plans to test this hypothesis using a random sample of 81 families from each suburb. His null hypothesis is ___.

a) σ₁² < σ₂²

b) μ₁ – µ₂ > 0

c) p₁ – p₂ = 0

d) μ₁ – μ₂ = 0

e) s₁ – s₂ = 0

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.

Section Reference: 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)

Bloom’s: Application

AACSB: Reflective Thinking

20. Restaurateur Denny Valentine is evaluating two sites, Raymondville and Rosenberg, for his next restaurant. He wants to prove that Raymondville residents (population 1) dine out more often than Rosenberg residents (population 2). Denny plans to test this hypothesis using a random sample of 81 families from each suburb. His alternate hypothesis is ___.

a) σ₁² < σ₂²

b) μ₁ – μ₂ > 0

c) p₁ – p₂ = 0

d) μ₁ – μ₂ = 0

e) s₁ – s₂ > 0

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.

Section Reference: 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)

Bloom’s: Application

AACSB: Reflective Thinking

21. Restaurateur Denny Valentine is evaluating two sites, Raymondville and Rosenberg, for his next restaurant. He wants to prove that Raymondville residents (population 1) dine out more often than Rosenberg residents (population 2). Denny commissions a market survey to test this hypothesis. The market researcher used a random sample of 64 families from each suburb, and reported the following: 1 = 15 times per month and 2 = 14 times per month. Assume that σ1 = 2 and σ2 = 3. With = .01, the critical z value is ___.

a) –1.96

b) 1.96

c) –2.33

d) –1.33

e) 2.33

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.

Section Reference: 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)

Bloom’s: Application

AACSB: Analytic

22. Restaurateur Denny Valentine is evaluating two sites, Raymondville and Rosenberg, for his next restaurant. He wants to prove that Raymondville residents (population 1) dine out more often than Rosenberg residents (population 2). Denny commissions a market survey to test this hypothesis. The market researcher used a random sample of 64 families from each suburb, and reported the following: 1 = 15 times per month and 2 = 14 times per month. Assume that σ1 = 2 and σ2 = 3. With = .01, the observed z value is ___.

a) 2.22

b) 12.81

c) 4.92

d) 3.58

e) 1.96

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.

Section Reference: 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)

Bloom’s: Application

AACSB: Analytic

23. Restaurateur Denny Valentine is evaluating two sites, Raymondville and Rosenberg, for his next restaurant. He wants to prove that Raymondville residents (population 1) dine out more often than Rosenberg residents (population 2). Denny commissions a market survey to test this hypothesis. The market researcher used a random sample of 64 families from each suburb, and reported the following: 1 = 15 times per month and 2 = 14 times per month. Assume that σ1 = 2 and σ2 = 3. With = .01, the appropriate decision is ___.

a) reject the null hypothesis σ₁² < σ₂²

b) accept the alternate hypothesis μ₁ – μ₂ > 0

c) reject the alternate hypothesis n1 = n2 = 64

d) fail to reject the null hypothesis μ₁ – μ₂ = 0

e) do nothing

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.

Section Reference: 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)

Bloom’s: Analysis

AACSB: Reflective Thinking

24. Restaurateur Denny Valentine is evaluating two sites, Raymondville and Rosenberg, for his next restaurant. He wants to prove that Raymondville residents (population 1) dine out more often than Rosenberg residents (population 2). Denny commissions a market survey to test this hypothesis. The market researcher used a random sample of 64 families from each suburb, and reported the following: 1 = 16 times per month and 2 = 14 times per month. Assume that σ1 = 4 and σ2 = 3. With = .01, the observed z value is ___.

a) 18.29

b) 6.05

c) 5.12

d) 3.40

e) 3.20

Difficulty: Hard

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.

Section Reference: 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)

Bloom’s: Application

AACSB: Analytic

25. Restaurateur Denny Valentine is evaluating two sites, Raymondville and Rosenberg, for his next restaurant. He wants to prove that Raymondville residents (population 1) dine out more often than Rosenberg residents (population 2). Denny commissions a market survey to test this hypothesis. The market researcher used a random sample of 64 families from each suburb, and reported the following: 1 = 16 times per month and 2 = 14 times per month. Assume that σ1 = 4 and σ2 = 3. With  = .01, the appropriate decision is ___.

a) do nothing

b) reject the null hypothesis σ1 < σ2

c) accept the alternate hypothesis μ₁ – μ₂ > 0

d) reject the alternate hypothesis n1 = n2 = 64

e) do not reject the null hypothesis μ₁ – μ₂ = 0

Difficulty: Hard

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.

Section Reference: 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)

Bloom’s: Analysis

AACSB: Reflective Thinking

26. Lucy Baker is analyzing demographic characteristics of two television programs, Lost (population 1) and Heroes (population 2). Previous studies indicate no difference in the ages of the two audiences. (The mean age of each audience is the same.) Lucy plans to test this hypothesis using a random sample of 100 from each audience. Her null hypothesis is ___.

a) μ₁ – μ₂ ≠ 0

b) μ₁ – μ₂ > 0

c) μ₁ – μ₂ = 0

d) μ₁ – μ₂ < 0

e) μ₁ – μ₂ < 1

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.

Section Reference: 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)

Bloom’s: Application

AACSB: Reflective Thinking

27. Lucy Baker is analyzing demographic characteristics of two television programs, Lost (population 1) and Heroes (population 2). Previous studies indicate no difference in the ages of the two audiences. (The mean age of each audience is the same.) Lucy plans to test this hypothesis using a random sample of 100 from each audience. Her alternate hypothesis is ___.

a) μ₁ – μ₂ < 0

b) μ₁ – μ₂ > 0

c) μ₁ – μ₂ = 0

d) μ₁ – μ₂ ≠ 0

e) μ₁ – μ₂ = 1

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.

Section Reference: 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)

Bloom’s: Application

AACSB: Reflective Thinking

28. Lucy Baker is analyzing demographic characteristics of two television programs, Lost (population 1) and Heroes (population 2). Previous studies indicate no difference in the ages of the two audiences. (The mean age of each audience is the same.) Her staff randomly selected 100 people from each audience, and reported the following: 1 = 43 years and 2 = 45 years. Assume that σ1 = 5 and σ2 = 8. With a two-tail test and  = .05, the critical z values are ___.

a) –1.64 and 1.64

b) –1.96 and 1.96

c) –2.33 and 2.33

d) –2.58 and 2.58

e) –2.97 and 2.97

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.

Section Reference: 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)

Bloom’s: Application

AACSB: Analytic

29. Lucy Baker is analyzing demographic characteristics of two television programs, Lost (population 1) and Heroes (population 2). Previous studies indicate no difference in the ages of the two audiences. (The mean age of each audience is the same.) Her staff randomly selected 100 people from each audience, and reported the following: 1 = 43 years and 2 = 45 years. Assume that σ1 = 5 and σ2 = 8. Assuming a two-tail test and  = .05, the observed z value is ___.

a) –2.12

b) –2.25

c) –5.58

d) –15.38

e) –20.68

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.

Section Reference: 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)

Bloom’s: Application

AACSB: Analytic

30. Lucy Baker is analyzing demographic characteristics of two television programs, Lost (population 1) and Heroes (population 2). Previous studies indicate no difference in the ages of the two audiences. (The mean age of each audience is the same.) Her staff randomly selected 100 people from each audience, and reported the following: 1 = 43 years and 2 = 45 years. Assume that σ1 = 5 and σ2 = 8. With a two-tail test and  = .05, the appropriate decision is ___.

a) do not reject the null hypothesis μ₁ – μ₂ = 0

b) reject the null hypothesis μ₁ – μ₂ > 0

c) reject the null hypothesis μ₁ – μ₂ = 0

d) do not reject the null hypothesis μ₁ – μ₂ < 0

e) do nothing

Difficulty: Hard

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.

Section Reference: 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)

Bloom’s: Analysis

AACSB: Reflective Thinking

31. A researcher wants to estimate the difference in the means of two populations. A random sample of 36 items from the first population results in a sample mean of 430. A random sample of 49 items from the second population results in a sample mean of 460. The population standard deviations are 120 for the first population and 140 for the second population. From this information, a 95% confidence interval for the difference in population means is ___.

a) –95.90 to 35.90

b) –85.44 to 25.44

c) –76.53 to 16.53

d) –102.83 to 42.43

e) 98.45 to 125.48

Difficulty: Hard

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.

Section Reference: 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)

Bloom’s: Application

AACSB: Analytic

32. A researcher is interested in testing to determine if the mean of population one is greater than the mean of population two. The null hypothesis is that there is no difference in the population means (i.e., the difference is zero). The alternative hypothesis is that there is a difference (i.e., the difference is not equal to zero). He randomly selects a sample of 9 items from population one resulting in a mean of 14.3 and a standard deviation of 3.4. He randomly selects a sample of 14 items from population two resulting in a mean of 11.8 and a standard deviation 2.9. He is using an alpha value of .10 to conduct this test. Assuming that the populations are normally distributed, the degrees of freedom for this problem are ___.

a) 23

b) 22

c) 21

d) 2

d) 1

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.

Bloom’s: Application

AACSB: Analytic

33. A researcher is interested in testing to determine if the mean of population one is greater than the mean of population two. The null hypothesis is that there is no difference in the population means (i.e., the difference is zero). The alternative hypothesis is that there is a difference (i.e., the difference is not equal to zero). He randomly selects a sample of 9 items from population one resulting in a mean of 14.3 and a standard deviation of 3.4. He randomly selects a sample of 14 items from population two resulting in a mean of 11.8 and a standard deviation 2.9. He is using an alpha value of .10 to conduct this test. Assuming that the populations are normally distributed, the critical t value from the table is ___.

a) 1.323

b) 1.721

c) 1.717

d) 1.321

e) 2.321

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.

Bloom’s: Application

AACSB: Analytic

34. A researcher wishes to determine the difference in two population means. To do this, she randomly samples 9 items from each population and computes a 90% confidence interval. The sample from the first population produces a mean of 780 with a standard deviation of 240. The sample from the second population produces a mean of 890 with a standard deviation of 280. Assume that the values are normally distributed in each population. The point estimate for the difference in the means of these two populations is ___.

a) –110

b) 40

c) –40

d) 0

e) 240

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.

Bloom’s: Application

AACSB: Analytic

35. A researcher wishes to determine the difference in two population means. To do this, she randomly samples 9 items from each population and computes a 90% confidence interval. The sample from the first population produces a mean of 780 with a standard deviation of 240. The sample from the second population produces a mean of 890 with a standard deviation of 280. Assume that the values are normally distributed in each population. The t value used for this is ___.

a) 1.860

b) 1.734

c) 1.746

d) 1.337

e) 2.342

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.

Bloom’s: Application

AACSB: Analytic

36. A researcher wants to conduct a before/after study on 11 subjects to determine if a treatment results in any difference in scores. The null hypothesis is that the average difference is zero while the alternative hypothesis is that the average difference is not zero. Scores are obtained on the subjects both before and after the treatment. After subtracting the after scores from the before scores, the average difference is computed to be ‑2.40 with a sample standard deviation of 1.21. Assume that the differences are normally distributed in the population. The degrees of freedom for this test are ___.

a) 11

b) 10

c) 9

d) 20

e) 2

Difficulty: Easy

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two dependent populations.

Section Reference: 10.3 Statistical Inferences for Two Related Populations

Bloom’s: Application

AACSB: Analytic

37. A researcher wants to conduct a before/after study on 11 subjects to determine if a treatment results in any difference in scores. The null hypothesis is that the average difference is zero while the alternative hypothesis is that the average difference is not zero. Scores are obtained on the subjects both before and after the treatment. After subtracting the after scores from the before scores, the average difference is computed to be ‑2.40 with a sample standard deviation of 1.21. Assume that the differences are normally distributed in the population. The observed t value for this test is ___.

a) –21.82

b) –6.58

c) –2.4

d) 1.98

e) 2.33

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two dependent populations.

Section Reference: 10.3 Statistical Inferences for Two Related Populations

Bloom’s: Application

AACSB: Analytic

38. A researcher wants to conduct a before/after study on 11 subjects to determine if a treatment results in any difference in scores. The null hypothesis is that the average difference is zero while the alternative hypothesis is that the average difference is not zero. Scores are obtained on the subjects both before and after the treatment. After subtracting the after scores from the before scores, the average difference is computed to be ‑2.40 with a sample standard deviation of 1.21. A 0.05 level of significance is selected. Assume that the differences are normally distributed in the population. The table t value for this test is ___.

a) 1.812

b) 2.228

c) 2.086

d) 2.262

e) 3.2467

Difficulty: Easy

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two dependent populations.

Section Reference: 10.3 Statistical Inferences for Two Related Populations

Bloom’s: Application

AACSB: Analytic

39. A researcher is conducting a matched-pairs study. She gathers data on each pair in the study resulting in:

Assume that the data are normally distributed in the population. The sample standard deviation (s) is ___.

a) 1.3

b) 1.14

c) 1.04

d) 1.02

e) 1.47

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two dependent populations.

Section Reference: 10.3 Statistical Inferences for Two Related Populations

Bloom’s: Application

AACSB: Analytic

40. A researcher is conducting a matched-pairs study. She gathers data on each pair in the study resulting in:

Assume that the data are normally distributed in the population. The degrees of freedom in this problem are ___.

a) 4

b) 8

c) 5

d) 9

e) 3

Difficulty: Easy

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two dependent populations.

Section Reference: 10.3 Statistical Inferences for Two Related Populations

Bloom’s: Application

AACSB: Analytic

41. A researcher is conducting a matched-pairs study. She gathers data on each pair in the study resulting in:

Assume that the data are normally distributed in the population. The level of significance is selected to be 0.10. If a two-tailed test is performed, the null hypothesis would be rejected if the observed value of t is ___.

a) less than –1.533 or greater than 1.533

b) less than –2.132 or greater than 2.132

c) less than –2.776 or greater than 2.776

d) less than –1.860 or greater than 1.860

e) less than –2.000 or greater than 2.000

Difficulty: Hard

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two dependent populations.

Section Reference: 10.3 Statistical Inferences for Two Related Populations

Bloom’s: Application

AACSB: Analytic

42. A researcher is conducting a matched-pairs study. She gathers data on each pair in the study resulting in:

Assume that the data are normally distributed in the population. The level of significance is selected to be 0.10. If the alternative hypothesis is that the average difference is greater than zero, the null hypothesis would be rejected if the observed value of t is ___.

a) greater than 1.533

b) less than –1.533

c) greater than 2.132

d) less than –2.132

e) equal to 2.333

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two dependent populations.

Section Reference: 10.3 Statistical Inferences for Two Related Populations

Bloom’s: Application

AACSB: Analytic

43. A researcher is estimating the average difference between two population means based on matched-pairs samples. She gathers data on each pair in the study resulting in:

Assume that the data are normally distributed in the population. To obtain a 95% confidence interval, the table t value would be ___.

a) 2.132

b) 1.86

c) 2.306

d) 2.976

e) 2.776

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two dependent populations.

Section Reference: 10.3 Statistical Inferences for Two Related Populations

Bloom’s: Application

AACSB: Analytic

44. A researcher is estimating the average difference between two population means based on matched-pairs samples. She gathers data on each pair in the study resulting in:

Assume that the data are normally distributed in the population. To obtain a 90% confidence interval, the table t value would be ___.

a) 1.86

b) 1.397

c) 1.533

d) 2.132

e) 3.346

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two dependent populations.

Section Reference: 10.3 Statistical Inferences for Two Related Populations

Bloom’s: Application

AACSB: Analytic

45. A researcher is estimating the average difference between two population means based on matched-pairs samples. She gathers data on each pair in the study resulting in:

Assume that the data are normally distributed in the population. A 95% confidence interval would be ___.

a) –3.02 to –0.18

b) –1.6 to –1.09

c) –2.11 to 1.09

d) –2.11 to –1.09

e) –3.23 to 2.23

Difficulty: Easy

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two dependent populations.

Section Reference: 10.3 Statistical Inferences for Two Related Populations

Bloom’s: Application

AACSB: Analytic

46. Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses. Her goal is 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. Her staff randomly selected 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 372 orders within 24 hours. Maureen's null hypothesis is ___.

a) p₁ – p₂ = 0

b) μ₁ – μ₂ = 0

c) p₁ – p₂ > 0

d) μ₁ – μ₂ < 0

e) μ₁ – μ₂ ≥ 0

Difficulty: Easy

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two population proportions.

Section Reference: 10.4 Statistical Inferences about Two Population Proportions, p₁ – p₂

Bloom’s: Application

AACSB: Reflective Thinking

47. Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses. Her goal is 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. Her staff randomly selected 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 372 orders within 24 hours. Maureen's alternate hypothesis is ___.

a) p₁ – p₂ ≠ 0

b) μ₁ – μ₂ > 0

c) p₁ – p₂ > 0

d) μ₁ – μ₂ ≠ 0

e) μ₁ – μ₂ ≥ 0

Difficulty: Easy

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two population proportions.

Section Reference: 10.4 Statistical Inferences about Two Population Proportions, p₁ – p₂

Bloom’s: Application

AACSB: Reflective Thinking

48. Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses. Her goal is 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. Her staff randomly selected 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 372 orders within 24 hours. Assuming  = 0.05, the critical z value is ___.

a) –1.96

b) –1.645

c) 1.645

d) 1.96

e) 2.33

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two population proportions.

Section Reference: 10.4 Statistical Inferences about Two Population Proportions, p₁ – p₂

Bloom’s: Application

AACSB: Analytic

49. Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses. Her goal is 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. Her staff randomly selected 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 372 orders within 24 hours. Assuming  = 0.05, the observed z value is ___.

a) –3.15

b) 2.42

c) 1.53

d) 0.95

e) 1.08

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two population proportions.

Section Reference: 10.4 Statistical Inferences about Two Population Proportions, p₁ – p₂

Bloom’s: Application

AACSB: Analytic

50. Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses. Her goal is 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. Her staff randomly selected 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 372 orders within 24 hours. Assuming  = 0.05, the appropriate decision is ___.

a) do not reject the null hypothesis μ₁ – μ₂ = 0

b) do not reject the null hypothesis p₁ – p₂ = 0

c) reject the null hypothesis μ₁ – μ₂ = 0

d) reject the null hypothesis p₁ – p₂ = 0

e) do not reject the null hypothesis p₁ – p₂ ≥ 0

Difficulty: Hard

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two population proportions.

Section Reference: 10.4 Statistical Inferences about Two Population Proportions, p₁ – p₂

Bloom’s: Analysis

AACSB: Reflective Thinking

51. Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses. Her goal is 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. Her staff randomly selected 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 356 orders within 24 hours. Assuming  = 0.05, the observed z value is ___.

a) –3.15

b) 2.42

c) 1.53

d) 0.95

e) 1.05

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two population proportions.

Section Reference: 10.4 Statistical Inferences about Two Population Proportions, p₁ – p₂

Bloom’s: Application

AACSB: Analytic

52. Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses. Her goal is 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. Her staff randomly selected 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 356 orders within 24 hours. Assuming  = 0.05, the appropriate decision is ___.

a) reject the null hypothesis p₁ – p₂ = 0

b) reject the null hypothesis μ₁ – μ₂ < 0

c) do not reject the null hypothesis μ₁ – μ₂ = 0

d) do not reject the null hypothesis p₁ – p₂ = 0

e) do not reject the null hypothesis p₁ – p₂ ≥ 0

Difficulty: Hard

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two population proportions.

Section Reference: 10.4 Statistical Inferences about Two Population Proportions, p₁ – p₂

Bloom’s: Analysis

AACSB: Reflective Thinking

53. Suppose that .06 of each of two populations possess a given characteristic. Samples of size 400 are randomly drawn from each population. The probability that the difference between the first sample proportion which possess the given characteristic and the second sample proportion which possess the given characteristic being more than +.03 is ___.

a) 0.4943

b) 0.9943

c) 0.0367

d) 0.5057

e) 0.5700

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two population proportions.

Section Reference: 10.4 Statistical Inferences about Two Population Proportions, p₁ – p₂

Bloom’s: Application

AACSB: Analytic

54. Suppose that .06 of each of two populations possess a given characteristic. Samples of size 400 are randomly drawn from each population. The standard deviation for the sampling distribution of differences between the first sample proportion and the second sample proportion (used to calculate the z score) is ___.

a) 0.00300

b) 0.01679

c) 0.05640

d) 0.00014

e) 0.12000

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two population proportions.

Section Reference: 10.4 Statistical Inferences about Two Population Proportions, p₁ – p₂

Bloom’s: Application

AACSB: Analytic

55. Suppose that .06 of each of two populations possess a given characteristic. Samples of size 400 are randomly drawn from each population. What is the probability that the differences in sample proportions will be greater than 0.02?

a) 0.4535

b) 0.9535

c) 0.1170

d) 0.5465

e) 0.4650

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two population proportions.

Section Reference: 10.4 Statistical Inferences about Two Population Proportions, p₁ – p₂

Bloom’s: Application

AACSB: Analytic

56. A statistician is being asked to test a new theory that the proportion of population A possessing a given characteristic is greater than the proportion of population B possessing the characteristic. A random sample of 600 from population A has been taken and it is determined that 480 possess the characteristic. A random sample of 700 taken from population B showed that 350 possess the characteristic. The observed z for this is ___.

a) 0.300

b) 0.624

c) 0.638

d) 11.22

e) 13.42

Difficulty: Easy

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two population proportions.

Section Reference: 10.4 Statistical Inferences about Two Population Proportions, p₁ – p₂

Bloom’s: Application

AACSB: Analytic

57. A researcher is interested in estimating the difference in two population proportions. A sample of 400 from each population results in sample proportions of .61 and .64. The point estimate of the difference in the population proportions is ___.

a) –0.030

b) 0.625

c) 0.000

d) 0.400

e) 0.500

Difficulty: Easy

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two population proportions.

Section Reference: 10.4 Statistical Inferences about Two Population Proportions, p₁ – p₂

Bloom’s: Application

AACSB: Analytic

58. A researcher is interested in estimating the difference in two population proportions. A sample of 400 from each population results in sample proportions of .61 and .64. A 90% confidence interval for the difference in the population proportions is ___.

a) –0.10 to 0.04

b) –0.09 to 0.03

c) –0.11 to 0.05

d) –0.07 to 0.01

e) –0.08 to 0.12

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two population proportions.

Section Reference: 10.4 Statistical Inferences about Two Population Proportions, p₁ – p₂

Bloom’s: Application

AACSB: Analytic

59. A random sample of 400 items from a population shows that 160 of the sample items possess a given characteristic. A random sample of 400 items from a second population resulted in 110 of the sample items possessing the characteristic. Using this data, a 99% confidence interval is constructed to estimate the difference in population proportions which possess the given characteristic. The resulting confidence interval is ___.

a) 0.06 to 0.19

b) 0.05 to 0.22

c) 0.09 to 0.16

d) 0.04 to 0.21

e) 0.05 to 0.23

Difficulty: Medium

Learning Objective: Test hypotheses and develop confidence intervals about the difference in two population proportions.

Section Reference: 10.4 Statistical Inferences about Two Population Proportions, p₁ – p₂

Bloom’s: Application

AACSB: Analytic

60. Collinsville Construction Company purchases steel rods for its projects. Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended purchasing rods from Redding Rods, Inc. (population 1), rather than Stockton Steel (population 2), since Redding's rods had less variability in length. Recently, Stockton revised its rod shearing operation, and Claude has sampled the outputs from Redding's and Stockton's rod manufacturing processes. The results for Redding were s₁² = 0.10 with n1 = 8, and, for Stockton, the results were s₂² = 0.05 with n2 = 10. Assume that rod lengths are normally distributed in the population. Claude's null hypothesis is ___.

a) σ_^σ_^

b) σ_^≠σ_^

c) σ_^σ_^

d) σ_^σ_^

e) s_^s_^

Difficulty: Easy

Learning Objective: Test hypotheses about the difference in two population variances using the F distribution.

Section Reference: 10.5 Testing Hypotheses about Two Population Variances

Bloom’s: Application

AACSB: Reflective Thinking

61. Collinsville Construction Company purchases steel rods for its projects. Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended purchasing rods from Redding Rods, Inc. (population 1), rather than Stockton Steel (population 2), since Redding's rods had less variability in length. Recently, Stockton revised its rod shearing operation, and Claude has sampled the outputs from Redding's and Stockton's rod manufacturing processes. The results for Redding were s₁² = 0.10 with n1 = 8, and, for Stockton, the results were s₂² = 0.05 with n2 = 10. Assume that rod lengths are normally distributed in the population. Claude's alternate hypothesis is ___.

a) σ_^σ_^

b) σ_^≠σ_^

c) σ_^σ_^

d) σ_^σ_^

e) s_^s_^

Difficulty: Easy

Learning Objective: Test hypotheses about the difference in two population variances using the F distribution.

Section Reference: 10.5 Testing Hypotheses about Two Population Variances

Bloom’s: Application

AACSB: Reflective Thinking

62. Collinsville Construction Company purchases steel rods for its projects. Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended purchasing rods from Redding Rods, Inc. (population 1), rather than Stockton Steel (population 2), since Redding's rods had less variability in length. Recently, Stockton revised its rod shearing operation, and Claude has sampled the outputs from Redding's and Stockton's rod manufacturing processes. The results for Redding were s₁² = 0.10 with n1 = 8, and, for Stockton, the results were s₂² = 0.05 with n2 = 10. Assume that rod lengths are normally distributed in the population. If  = 0.05, the critical F value is ___.

a) 3.68

b) 3.29

c) 3.50

d) 3.79

e) 3.99

Difficulty: Easy

Learning Objective: Test hypotheses about the difference in two population variances using the F distribution.

Section Reference: 10.5 Testing Hypotheses about Two Population Variances

Bloom’s: Application

AACSB: Analytic

63. Collinsville Construction Company purchases steel rods for its projects. Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended purchasing rods from Redding Rods, Inc. (population 1), rather than Stockton Steel (population 2), since Redding's rods had less variability in length. Recently, Stockton revised its rod shearing operation, and Claude has sampled the outputs from Redding's and Stockton's rod manufacturing processes. The results for Redding were s₁² = 0.10 with n1 = 8, and, for Stockton, the results were s₂² = 0.05 with n2 = 10. Assume that rod lengths are normally distributed in the population. If = 0.05, the observed F value is ___.

a) 0.50

b) 2.00

c) 1.41

d) 0.91

e) 0.71

Difficulty: Medium

Learning Objective: Test hypotheses about the difference in two population variances using the F distribution.

Section Reference: 10.5 Testing Hypotheses about Two Population Variances

Bloom’s: Application

AACSB: Analytic

64. Collinsville Construction Company purchases steel rods for its projects. Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended purchasing rods from Redding Rods, Inc. (population 1), rather than Stockton Steel (population 2), since Redding's rods had less variability in length. Recently, Stockton revised its rod shearing operation, and Claude has sampled the outputs from Redding's and Stockton's rod manufacturing processes. The results for Redding were s₁² = 0.10 with n1 = 8, and, for Stockton, the results were s₂² = 0.05 with n2 = 10. Assume that rod lengths are normally distributed in the population If = 0.05, the appropriate decision is ___.

a) reject the null hypothesisσ_^σ_^

b) reject the null hypothesis σ_^σ_^

c) do not reject the null hypothesisσ_^σ_^

d) do not reject the null hypothesisσ_^σ_^

e) do nothing

Difficulty: Hard

Learning Objective: Test hypotheses about the difference in two population variances using the F distribution.

Section Reference: 10.5 Testing Hypotheses about Two Population Variances

Bloom’s: Analysis

AACSB: Reflective Thinking

65. Collinsville Construction Company purchases steel rods for its projects. Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended purchasing rods from Redding Rods, Inc. (population 1), rather than Stockton Steel (population 2), since Redding's rods had less variability in length. Recently, Stockton revised its rod shearing operation, and Claude has sampled the outputs from Redding's and Stockton's rod manufacturing processes. The results for Redding were s₁² = 0.15 with n1 = 8, and, for Stockton, the results were s₂² = 0.04 with n2 = 10. Assume that rod lengths are normally distributed in the population If = 0.05, the observed F value is ___.

a) 0.27

b) 0.52

c) 1.92

d) 3.75

e) 4.25

Difficulty: Medium

Learning Objective: Test hypotheses about the difference in two population variances using the F distribution.

Section Reference: 10.5 Testing Hypotheses about Two Population Variances

Bloom’s: Application

AACSB: Analytic

66. Collinsville Construction Company purchases steel rods for its projects. Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended purchasing rods from Redding Rods, Inc. (population 1), rather than Stockton Steel (population 2), since Redding's rods had less variability in length. Recently, Stockton revised its rod shearing operation, and Claude has sampled the outputs from Redding's and Stockton's rod manufacturing processes. The results for Redding were s₁² = 0.15 with n1 = 8, and, for Stockton, the results were s₂² = 0.05 with n2 = 10. Assume that rod lengths are normally distributed in the population. If = 0.05, the appropriate decision is ___.

a) reject the null hypothesisσ_^σ_^

b) reject the null hypothesis σ_^σ_^

c) do not reject the null hypothesisσ_^σ_^

d) do not reject the null hypothesisσ_^σ_^

e) do nothing

Difficulty: Hard

Learning Objective: Test hypotheses about the difference in two population variances using the F distribution.

Section Reference: 10.5 Testing Hypotheses about Two Population Variances

Bloom’s: Analysis

AACSB: Reflective Thinking

67. Tamara Hill, fund manager of the Hill Value Fund, manages a portfolio of 250 common stocks. Tamara is searching for a 'low risk' issue to add to the portfolio, i.e., one with a price variance less than that of the S&P 500 index. Moreover, she assumes an issue is not 'low risk' until demonstrated otherwise. Her staff reported that during the last nine quarters the price variance for the S&P 500 index (population 1) was 25, and for the last seven quarters the price variance for XYC common (population 2) was 8. Assume that stock prices are normally distributed in the population. Using = 0.05, Tamara's null hypothesis is ___.

a) σ_^σ_^

b) σ_^≠σ_^

c) σ_^σ_^

d) σ_^σ_^

e) s_^s_^

Difficulty: Easy

Learning Objective: Test hypotheses about the difference in two population variances using the F distribution.

Section Reference: 10.5 Testing Hypotheses about Two Population Variances

Bloom’s: Application

AACSB: Reflective Thinking

68. Tamara Hill, fund manager of the Hill Value Fund, manages a portfolio of 250 common stocks. Tamara is searching for a 'low risk' issue to add to the portfolio, i.e., one with a price variance less than that of the S&P 500 index. Moreover, she assumes an issue is not 'low risk' until demonstrated otherwise. Her staff reported that during the last nine quarters the price variance for the S&P 500 index (population 1) was 25, and for the last seven quarters the price variance for XYC common (population 2) was 8. Assume that stock prices are normally distributed in the population. Using  = 0.05, Tamara's alternate hypothesis is ___.

a) σ_^σ_^

b) σ_^≠σ_^

c) σ_^σ_^

d) σ_^σ_^

e) s_^s_^

Difficulty: Easy

Learning Objective: Test hypotheses about the difference in two population variances using the F distribution.

Section Reference: 10.5 Testing Hypotheses about Two Population Variances

Bloom’s: Application

AACSB: Reflective Thinking

69. Tamara Hill, fund manager of the Hill Value Fund, manages a portfolio of 250 common stocks. Tamara is searching for a 'low risk' issue to add to the portfolio, i.e., one with a price variance less than that of the S&P 500 index. Moreover, she assumes an issue is not 'low risk' until demonstrated otherwise. Her staff reported that during the last nine quarters the price variance for the S&P 500 index (population 1) was 25, and for the last seven quarters the price variance for XYC common (population 2) was 8. Assume that stock prices are normally distributed in the population. Using  = 0.05, the critical F value is ___.

a) 3.68

b) 3.58

c) 4.15

d) 3.29

e) 4.89

Difficulty: Hard

Learning Objective: Test hypotheses about the difference in two population variances using the F distribution.

Section Reference: 10.5 Testing Hypotheses about Two Population Variances

Bloom’s: Application

AACSB: Analytic

70. Tamara Hill, fund manager of the Hill Value Fund, manages a portfolio of 250 common stocks. Tamara is searching for a 'low risk' issue to add to the portfolio, i.e., one with a price variance less than that of the S&P 500 index. Moreover, she assumes an issue is not 'low risk' until demonstrated otherwise. Her staff reported that during the last nine quarters the price variance for the S&P 500 index (population 1) was 25, and for the last seven quarters the price variance for XYC common (population 2) was 8. Assume that stock prices are normally distributed in the population. Using  = 0.05, the observed F value is ___.

a) 3.13

b) 0.32

c) 1.77

d) 9.77

e) 9.87

Difficulty: Medium

Learning Objective: Test hypotheses about the difference in two population variances using the F distribution.

Section Reference: 10.5 Testing Hypotheses about Two Population Variances

Bloom’s: Application

AACSB: Analytic

71. Tamara Hill, fund manager of the Hill Value Fund, manages a portfolio of 250 common stocks. Tamara is searching for a 'low risk' issue to add to the portfolio, i.e., one with a price variance less than that of the S&P 500 index. Moreover, she assumes an issue is not 'low risk' until demonstrated otherwise. Her staff reported that during the last nine quarters the price variance for the S&P 500 index (population 1) was 25, and for the last seven quarters the price variance for XYC common (population 2) was 8. Assume that stock prices are normally distributed in the population. Using = 0.05, the appropriate decision is ___.

a) reject the null hypothesis σ_^σ_^

b) reject the null hypothesis σ_^≠σ_^

c) do not reject the null hypothesisσ_^σ_^

d) do not reject the null hypothesisσ_^≠σ_^

e) do nothing

Difficulty: Hard

Learning Objective: Test hypotheses about the difference in two population variances using the F distribution.

Section Reference: 10.5 Testing Hypotheses about Two Population Variances

Bloom’s: Analysis

AACSB: Reflective Thinking

72. Tamara Hill, fund manager of the Hill Value Fund, manages a portfolio of 250 common stocks. Tamara is searching for a 'low risk' issue to add to the portfolio, i.e., one with a price variance less than that of the S&P 500 index. Moreover, she assumes an issue is not 'low risk' until demonstrated otherwise. Her staff reported that during the last nine quarters the price variance for the S&P 500 index (population 1) was 25, and for the last seven quarters the price variance for XYC common (population 2) was 6. Assume that stock prices are normally distributed in the population. Using  = 0.05, the observed F value is ___.

a) 17.36

b) 2.04

c) 0.24

d) 4.77

e) 4.17

Difficulty: Medium

Learning Objective: Test hypotheses about the difference in two population variances using the F distribution.

Section Reference: 10.5 Testing Hypotheses about Two Population Variances

Bloom’s: Application

AACSB: Analytic

73. Tamara Hill, fund manager of the Hill Value Fund, manages a portfolio of 250 common stocks. Tamara is searching for a 'low risk' issue to add to the portfolio, i.e., one with a price variance less than that of the S&P 500 index. Moreover, she assumes an issue is not 'low risk' until demonstrated otherwise. Her staff reported that during the last nine quarters the price variance for the S&P 500 index (population 1) was 25, and for the last seven quarters the price variance for XYC common (population 2) was 6. Assume that stock prices are normally distributed in the population. Using  = 0.05, the appropriate decision is ___.

a) reject the null hypothesis σ_^σ_^

b) reject the null hypothesis σ_^≠σ_^

c) do not reject the null hypothesisσ_^σ_^

d) do not reject the null hypothesisσ_^≠σ_^

e) maintain status quo

Difficulty: Hard

Learning Objective: Test hypotheses about the difference in two population variances using the F distribution.

Section Reference: 10.5 Testing Hypotheses about Two Population Variances

Bloom’s: Analysis

AACSB: Reflective Thinking

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