Ch10 – Statistical Inferences About Two | Verified Test Bank - Business Stats Contemporary Decision 10e | Test Bank by Ken Black by Ken Black. DOCX document preview.
File: Ch10, Chapter 10: Statistical Inferences about Two Populations
True/False
1. An appropriate sampling plan to determine if there is a difference in the speed of a wireless router from two different manufacturers, consists of a network manager drawing independent samples of wireless routers from the two manufacturers and comparing the difference in the sample means for the connection speed.
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Easy
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
2. The difference in two sample means is normally distributed for sample sizes ≥ 30, only if the populations are normally distributed.
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Easy
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
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.
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Medium
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
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.
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Medium
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
5. If a 98% confidence interval for the difference in the two population means does not contain zero, then the null hypothesis of a zero difference between the two population means cannot be rejected at a 0.02 level of significance.
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Hard
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
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.
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Hard
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
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: 10.2: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.
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: 10.2: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.
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: 10.2: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.
10. If the populations are normally distributed and 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: 10.2: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.
11. If the populations are normally distributed and 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: 10.2: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.
12. In order to construct an interval estimate of 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 -1) degrees of freedom.
Difficulty: Medium
Learning Objective: 10.2: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.
13. In order to construct an interval estimate of 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: 10.2: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.
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.
Response: See section 10.3 Statistical Inferences for Two Related Populations
Difficulty: Easy
Learning Objective: 10.3: Test hypotheses and develop confidence intervals about the difference in two dependent populations.
15. Hypothesis tests conducted on sets of matched samples are sometimes referred to as correlated t tests.
Response: See section 10.3 Statistical Inferences for Two Related Populations
Difficulty: Easy
Learning Objective: 10.3: Test hypotheses and develop confidence intervals about the difference in two dependent populations.
16. Sets of matched samples are also referred to as dependent samples.
Response: See section 10.3 Statistical Inferences for Two Related Populations
Difficulty: Easy
Learning Objective: 10.3: Test hypotheses and develop confidence intervals about the difference in two dependent populations.
17. In conducting a matched-pairs hypothesis test, the null and alternative hypotheses always represent one-tailed tests.
Response: See section 10.3 Statistical Inferences for Two Related Populations
Difficulty: Easy
Learning Objective: 10.3: Test hypotheses and develop confidence intervals about the difference in two dependent populations.
18. When testing for the difference between two population proportions we use a pooled estimate of the proportion.
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 – p2
Difficulty: Medium
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
19. When finding a confidence interval for the difference between two population proportions we use a pooled estimate of the proportion.
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 – p2
Difficulty: Medium
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
20. Testing the difference in two population proportions is useful whenever the researcher is interested in comparing the proportion of one population that has certain characteristic with the proportion of the second population that has the same characteristic.
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 – p2
Difficulty: Easy
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
21. 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.
Response: See section 10.5 Testing Hypotheses about Two Population Variances
Difficulty: Medium
Learning Objective: 10.5: Test hypotheses about the difference in two population variances using the F distribution.
22. The F test of two population variances is extremely robust to the violations of the assumption that the populations are normally distributed.
Response: See section 10.5 Testing Hypotheses about Two Population Variances
Difficulty: Medium
Learning Objective: 10.5: Test hypotheses about the difference in two population variances using the F distribution.
23. The F statistic is a ratio of two independent sample variances.
Response: See section 10.5 Testing Hypotheses about Two Population Variances
Difficulty: Medium
Learning Objective: 10.5: Test hypotheses about the difference in two population variances using the F distribution
24. The ratio of two independent sample variances follows the F distribution.
Response: See section 10.5 Testing Hypotheses about Two Population Variances
Difficulty: Medium
Learning Objective: 10.5: Test hypotheses about the difference in two population variances using the F distribution
Multiple Choice
25. Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course. He wants to prove that Palmetto Dunes residents (population 1) play golf more often than Ocean Greens residents (population 2). Roberto plans to test this hypothesis using a random sample of 81 individuals from each suburb. His null hypothesis is __________.
a) σ12 < σ22
b) μ1- 2
c) p1 – p2 = 0
d) μ1 - μ2 ≤ 0
e) s1 – s2 = 0
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Medium
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
26. Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course. He wants to prove that Palmetto Dunes residents (population 1) play golf more often than Ocean Greens residents (population 2). Roberto plans to test this hypothesis using a random sample of 81 individuals from each suburb. His alternative hypothesis is __________.
a) σ12 < σ22
b) μ1- 2
c) p1 – p2 = 0
d) μ1 - μ2 = 0
e) s1 – s2 > 0
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Medium
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
27. Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course. He wants to prove that Palmetto Dunes residents (population 1) play golf more often than Ocean Greens residents (population 2). Roberto commissions a market survey to test this hypothesis. The market researcher used a random sample of 64 individuals 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
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Medium
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
28. Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course. He wants to prove that Palmetto Dunes residents (population 1) play golf more often than Ocean Greens residents (population 2). Roberto commissions a market survey to test this hypothesis. The market researcher used a random sample of 64 individuals 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
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Medium
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
29. Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course. He wants to prove that Palmetto Dunes residents (population 1) play golf more often than Ocean Greens residents (population 2). Roberto commissions a market survey to test this hypothesis. The market researcher used a random sample of 64 individuals 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- 2
c) reject the alternate hypothesis n1 = n2 = 64
d) fail to reject the null hypothesis μ1 - μ2 = 0
e) do nothing
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Medium
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
30. Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course. He wants to prove that Palmetto Dunes residents (population 1) play golf more often than Ocean Greens residents (population 2). Roberto commissions a market survey to test this hypothesis. The market researcher used a random sample of 64 individuals 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
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Medium
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
31. Golf course designer Roberto Langabeer is evaluating two sites, Palmetto Dunes and Ocean Greens, for his next golf course. He wants to prove that Palmetto Dunes residents (population 1) play golf more often than Ocean Greens residents (population 2). Roberto commissions a market survey to test this hypothesis. The market researcher used a random sample of individuals 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 1 < 2
c) accept the alternate hypothesis μ1- 2
d) reject the alternate hypothesis n1 = n2 = 64
e) do not reject the null hypothesis μ1 - μ2 = 0
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Medium
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
32. Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1) and 60 Minutes (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
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Medium
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
33. Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1) and 60 Minutes (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
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Medium
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
34. Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1) and 60 Minutes (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
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Medium
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
35. Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1) and 60 Minutes (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
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Medium
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
36. Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1) and 60 Minutes (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 hypothesisμ1 - μ2 = 0
b) reject the null hypothesis μ1 - μ2 > 0
c) reject the null hypothesis μ1 - μ2 = 0
d) do not reject the null hypothesisμ1 - μ2 < 0
e) do nothing
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Hard
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
37. 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, 25.44
c) -76.53 to 16.53
d) -102.83 to 42.43
e) 98.45 to 125.48
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Hard
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
38. A researcher is interested in testing to determine if the mean price of a casual lunch is different in the city than it is in the suburbs. 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 lunch tickets from the city population resulting in a mean of $14.30 and a standard deviation of $3.40. He randomly selects a sample of 14 lunch tickets from the suburban population resulting in a mean of $11.80 and a standard deviation $2.90. He is using an alpha value of .10 to conduct this test. Assuming that the populations are normally distributed and that the population variances are approximately equal, the degrees of freedom for this problem are _______.
a) 23
b) 22
c) 21
d) 2
d) 1
Difficulty: Medium
Learning Objective: 10.2: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.
39. A researcher is interested in testing to determine if the mean price of a casual lunch is different in the city than it is in the suburbs. 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 lunch tickets from the city population resulting in a mean of $14.30 and a standard deviation of $3.40. He randomly selects a sample of 14 lunch tickets from the suburban population resulting in a mean of $11.80 and a standard deviation $2.90. 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: 10.2: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.
40. 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: Easy
Learning Objective: 10.2: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.
41. 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 and that the population variances are approximately equal. The critical t value used from the table for this is _______.
a) 1.860
b) 1.734
c) 1.746
d) 1.337
e) 2.342
Difficulty: Medium
Learning Objective: 10.2: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.
42. A researcher believes a new diet should improve weight gain. To test his hypothesis a random sample of 10 people on the old diet and an independent random sample of 10 people on the new diet were selected. The selected people on the old diet gain an average of 5 pounds with a standard deviation of 2 pounds, while the average gain for selected people on the new diet was 8 pounds with a standard deviation of 1.5 pounds. Assume that the values are normally distributed in each population and that the population variances are approximately equal. Using = 0.05, the critical t value used from the table for this is _______.
a) -1.96
b) -1.645
c) -2.100
d) -3.79
e) -1.734
Difficulty: Medium
Learning Objective: 10.2: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.
43. A researcher believes a new diet should improve weight gain. To test his hypothesis a random sample of 10 people on the old diet and an independent random sample of 10 people on the new diet were selected. The selected people on the old diet gain an average of 5 pounds with a standard deviation of 2 pounds, while the average gain for selected people on the new diet was 8 pounds with a standard deviation of 1.5 pounds. Assume that the values are normally distributed in each population and that the population variances are approximately equal. Using = 0.05, the observed t value for this test is _______.
a) -1.96
b) -1.645
c) -2.100
d) -3.79
e) -1.734
Difficulty: Medium
Learning Objective: 10.2: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.
44. A researcher wants to conduct a before/after study on 11 subjects to determine if a new cholesterol medication results in higher HDL cholesterol readings. 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 taking the medication. 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
Response: See section 10.3 Statistical Inferences for Two Related Populations
Difficulty: Easy
Learning Objective: 10.3: Test hypotheses and develop confidence intervals about the difference in two dependent populations.
45. A researcher wants to conduct a before/after study on 11 subjects to determine if a new cholesterol medication results in higher HDL cholesterol readings. 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 taking the medication. 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
Response: See section 10.3 Statistical Inferences for Two Related Populations
Difficulty: Medium
Learning Objective: 10.3: Test hypotheses and develop confidence intervals about the difference in two dependent populations.
46. A researcher wants to conduct a before/after study on 11 subjects to determine if a new cholesterol medication results in higher HDL cholesterol readings. 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 taking the medication. 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
Response: See section 10.3 Statistical Inferences for Two Related Populations
Difficulty: Easy
Learning Objective: 10.3: Test hypotheses and develop confidence intervals about the difference in two dependent populations.
47. A researcher is conducting a matched‑pairs study. She gathers data on each pair in the study resulting in:
Pair | Group 1 | Group 2 |
1 | 10 | 12 |
2 | 8 | 9 |
3 | 11 | 11 |
4 | 8 | 10 |
5 | 9 | 12 |
Assume that the data are normally distributed in the population. The sample standard deviation (sd) of the differences is _______.
a) 1.30
b) 1.14
c) 1.04
d) 1.02
e) 1.47
Response: See section 10.3 Statistical Inferences for Two Related Populations
Difficulty: Medium
Learning Objective: 10.3: Test hypotheses and develop confidence intervals about the difference in two dependent populations.
48. A researcher is conducting a matched‑pairs study. She gathers data on each pair in the study resulting in:
Pair | Group 1 | Group 2 |
1 | 10 | 12 |
2 | 8 | 9 |
3 | 11 | 11 |
4 | 8 | 10 |
5 | 9 | 12 |
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
Response: See section 10.3 Statistical Inferences for Two Related Populations
Difficulty: Easy
Learning Objective: 10.3: Test hypotheses and develop confidence intervals about the difference in two dependent populations.
49. A researcher is conducting a matched‑pairs study. She gathers data on each pair in the study resulting in:
Pair | Group 1 | Group 2 |
1 | 10 | 12 |
2 | 8 | 9 |
3 | 11 | 11 |
4 | 8 | 10 |
5 | 9 | 12 |
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
Response: See section 10.3 Statistical Inferences for Two Related Populations
Difficulty: Medium
Learning Objective: 10.3: Test hypotheses and develop confidence intervals about the difference in two dependent populations.
50. A researcher is conducting a matched‑pairs study. She gathers data on each pair in the study resulting in:
Pair | Group 1 | Group 2 |
1 | 10 | 12 |
2 | 8 | 9 |
3 | 11 | 11 |
4 | 8 | 10 |
5 | 9 | 12 |
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
Response: See section 10.3 Statistical Inferences for Two Related Populations
Difficulty: Medium
Learning Objective: 10.3: Test hypotheses and develop confidence intervals about the difference in two dependent populations.
51. 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:
Pair | Group 1 | Group 2 |
1 | 10 | 12 |
2 | 8 | 9 |
3 | 11 | 11 |
4 | 8 | 10 |
5 | 9 | 12 |
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
Response: See section 10.3 Statistical Inferences for Two Related Populations
Difficulty: Medium
Learning Objective: 10.3: Test hypotheses and develop confidence intervals about the difference in two dependent populations.
52. 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:
Pair | Group 1 | Group 2 |
1 | 10 | 12 |
2 | 8 | 9 |
3 | 11 | 11 |
4 | 8 | 10 |
5 | 9 | 12 |
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
Response: See section 10.3 Statistical Inferences for Two Related Populations
Difficulty: Medium
Learning Objective: 10.3: Test hypotheses and develop confidence intervals about the difference in two dependent populations.
53. 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:
Pair | Group 1 | Group 2 |
1 | 10 | 12 |
2 | 8 | 9 |
3 | 11 | 11 |
4 | 8 | 10 |
5 | 9 | 12 |
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
Response: See section 10.3 Statistical Inferences for Two Related Populations
Difficulty: Medium
Learning Objective: 10.3: Test hypotheses and develop confidence intervals about the difference in two dependent populations.
54. 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
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 – p2
Difficulty: Easy
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
55. 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 West Coast Warehouse has consistently out-performed the East 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 alternative hypothesis is _______.
a) p1 – p2 ≠ 0
b) μ1 - μ2 > 0
c) p1 – p2 > 0
d) μ1 - μ2 ≠ 0
e) μ1 - μ2 ≥ 0
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 – p2
Difficulty: Easy
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
56. 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 West Coast Warehouse has consistently out-performed the East 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) -1.64
c) 1.64
d) 1.96
e) 2.33
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 – p2
Difficulty: Medium
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
57. 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 West Coast Warehouse has consistently out-performed the East 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
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 – p2
Difficulty: Medium
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
58. 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 West Coast Warehouse has consistently out-performed the East 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
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 – p2
Difficulty: Hard
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
59. 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 West Coast Warehouse has consistently out-performed the East 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
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 – p2
Difficulty: Medium
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
60. 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 West Coast Warehouse has consistently out-performed the East 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
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 – p2
Difficulty: Hard
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
61. 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
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 – p2
Difficulty: Hard
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
62. 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
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 – p2
Difficulty: Medium
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
63. 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
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 – p2
Difficulty: Hard
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
64. A university administrator believes that business students are more likely to be working and going to school than their liberal arts majors. This information may lead to the business school offering courses in the evening hours while the liberal arts college maintains a daytime schedule. To test this theory, the proportion of business students who are working at least 20 hours per week is compared to the proportion of liberal arts students who are working at least 20 hours per week. A random sample of 600 from the business school has been taken and it is determined that 480 students work at least 20 hours per week. A random sample of 700 liberal arts students showed that 350 work at least 20 hours per week. The observed z for this is _______.
a) 0.300
b) 0.624
c) 0.638
d) 11.22
e) 13.42
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 – p2
Difficulty: Medium
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
65. 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
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 – p2
Difficulty: Easy
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
66. 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
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 – p2
Difficulty: Medium
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
67. 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 these 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
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 – p2
Difficulty: Medium
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
68. Collinsville Construction Company purchases steel rods for its projects. Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended not purchasing rods from Redding Rods, Inc. (population 1), and switching to Stockton Steel (population 2), since Stockton’s rods had less variability in length. 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) σσ
d) σσ
e) ss
Response: See section 10.5 Testing Hypotheses about Two Population Variances
Difficulty: Easy
Learning Objective: 10.5: Test hypotheses about the difference in two population variances using the F distribution
69. Collinsville Construction Company purchases steel rods for its projects. Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended not purchasing rods from Redding Rods, Inc. (population 1), and switching to Stockton Steel (population 2), since Stockton’s rods had less variability in length. 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 alternative hypothesis is _____________.
a) σσ
b) σ≠σ
c) σσ
d) σσ
e) ss
Response: See section 10.5 Testing Hypotheses about Two Population Variances
Difficulty: Easy
Learning Objective: 10.5: Test hypotheses about the difference in two population variances using the F distribution.
70. Collinsville Construction Company purchases steel rods for its projects. Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended not purchasing rods from Redding Rods, Inc. (population 1), and switching to Stockton Steel (population 2), since Stockton’s rods had less variability in length. 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
Response: See section 10.5 Testing Hypotheses about Two Population Variances
Difficulty: Easy
Learning Objective: 10.5: Test hypotheses about the difference in two population variances using the F distribution.
71. Collinsville Construction Company purchases steel rods for its projects. Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended not purchasing rods from Redding Rods, Inc. (population 1), and switching to Stockton Steel (population 2), since Stockton’s rods had less variability in length. 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
Response: See section 10.5 Testing Hypotheses about Two Population Variances
Difficulty: Medium
Learning Objective: 10.5: Test hypotheses about the difference in two population variances using the F distribution.
72. Collinsville Construction Company purchases steel rods for its projects. Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended not purchasing rods from Redding Rods, Inc. (population 1), and switching to Stockton Steel (population 2), since Stockton’s rods had less variability in length. 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 hypothesisσσ
b) reject the null hypothesis σσ
c) do not reject the null hypothesisσ≤σ
d) do not reject the null hypothesisσσ
e) do nothing
Response: See section 10.5 Testing Hypotheses about Two Population Variances
Difficulty: Hard
Learning Objective: 10.5: Test hypotheses about the difference in two population variances using the F distribution.
73. Collinsville Construction Company purchases steel rods for its projects. Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended not purchasing rods from Redding Rods, Inc. (population 1), and switching to Stockton Steel (population 2), since Stockton’s rods had less variability in length. 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
Response: See section 10.5 Testing Hypotheses about Two Population Variances
Difficulty: Medium
Learning Objective: 10.5: Test hypotheses about the difference in two population variances using the F distribution.
74. Collinsville Construction Company purchases steel rods for its projects. Based on previous tests, Claude Carter, Quality Assurance Manager, has recommended not purchasing rods from Redding Rods, Inc. (population 1), and switching to Stockton Steel (population 2), since Redding’s rods had more variability in length. 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 hypothesisσ≤=σ
b) reject the null hypothesis σσ
c) do not reject the null hypothesisσσ
d) do not reject the null hypothesisσσ
e) do nothing
Response: See section 10.5 Testing Hypotheses about Two Population Variances
Difficulty: Hard
Learning Objective: 10.5: Test hypotheses about the difference in two population variances using the F distribution.
75. 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) σσ
d) σσ
e) ss
Response: See section 10.5 Testing Hypotheses about Two Population Variances
Difficulty: Easy
Learning Objective: 10.5: Test hypotheses about the difference in two population variances using the F distribution.
76. 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) σσ
b) σ≠σ
c) σσ
d) σσ
e) ss
Response: See section 10.5 Testing Hypotheses about Two Population Variances
Difficulty: Easy
Learning Objective: 10.5: Test hypotheses about the difference in two population variances using the F distribution.
77. 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
Response: See section 10.5 Testing Hypotheses about Two Population Variances
Difficulty: Easy
Learning Objective: 10.5: Test hypotheses about the difference in two population variances using the F distribution.
78. 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
Response: See section 10.5 Testing Hypotheses about Two Population Variances
Difficulty: Medium
Learning Objective: 10.5: Test hypotheses about the difference in two population variances using the F distribution.
79. 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 σσ
b) reject the null hypothesis σ≠σ
c) do not reject the null hypothesisσ≤σ
d) do not reject the null hypothesisσ≠σ
e) do nothing
Response: See section 10.5 Testing Hypotheses about Two Population Variances
Difficulty: Hard
Learning Objective: 10.5: Test hypotheses about the difference in two population variances using the F distribution
80. 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
Response: See section 10.5 Testing Hypotheses about Two Population Variances
Difficulty: Medium
Learning Objective: 10.5: Test hypotheses about the difference in two population variances using the F distribution
81. 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 hypothesisσσ
d) do not reject the null hypothesisσ≠σ
e) maintain status quo
Response: See section 10.5 Testing Hypotheses about Two Population Variances
Difficulty: Hard
Learning Objective: 10.5: Test hypotheses about the difference in two population variances using the F distribution.
82. A researcher believes a new diet should improve weight gain. To test his hypothesis, a random sample of 10 people on the old diet and an independent random sample of 10 people on the new diet were selected. The selected people on the old diet gained an average of 5 pounds with a standard deviation of 2 pounds, while the average gain for selected people on the new diet was 8 pounds with a standard deviation of 1.5 pounds. Assuming that the values are normally distributed in each population, the researcher would like to use the t procedure with pooled standard deviation. To use this procedure, it must be shown that the variances from the two populations can be assumed to be equal. Using the sample data to test this assumption at = 0.05, the observed F value is _______.
a) 1.78
b) 3.79
c) -3.79
d) 3.18
e) 1.33
Response: See section 10.5 Testing Hypotheses about Two Population Variances
Difficulty: Medium
Learning Objective: 10.5: Test hypotheses about the difference in two population variances using the F distribution
83. Your company is evaluating two cloud-based, secured data storage services. “Pie in the Sky,” the newer service, claims its uploading and downloading speeds are faster than the older service, “Cloudy but Steady Skies.” You need to make a decision based on published access times for both services at different times and for varying file sizes. Your alternative hypothesis is ______.
a) σ12 < σ22
b) μ1 − 2
c) p1 − p2 = 0
d) μ1 − μ2 = 0
e) s1 − s2 = 0
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
84. Your company is evaluating two cloud-based secured data storage services. “Pie in the Sky,” the newer service, claims its uploading and downloading speeds are faster than the older service, “Cloudy but Steady Skies.” You need to make a decision based on published access times for both services at different times and for varying file sizes. To make your decision, you purchase a statistical study, which indicates that the average download time for Pie in the Sky is 0.77 sec. per MB and for Cloudy but Steady Skies is 0.84. Assume that σ1 = 0.2 and σ2 = 0.3. With = .05, the critical z value is ______.
a) 1.645
b) −1.645
c) 1.96
d) −1.96
e) 2.33
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
85. Your company is evaluating two cloud-based secured data storage services. “Pie in the Sky,” the newer service, claims its uploading and downloading speeds are faster than the older service, “Cloudy but Steady Skies.” You need to make a decision based on published access times for both services at different times and for varying file sizes. To make your decision, you purchase a statistical study, which indicates that the average download time for Pie in the Sky is 0.77 sec. per MB and for Cloudy but Steady Skies is 0.84. Assume that n1 = n2 = 50, σ1 = 0.2 and σ2 = 0.3. With = .05, the observed z value is ______.
a) −9.71
b) −1.37
c) −0.7
d) 1.37
e) 1.96
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
86. Your company is evaluating two cloud-based secured data storage services. “Pie in the Sky,” the newer service, claims its uploading and downloading speeds are faster than the older service, “Cloudy but Steady Skies.” You need to make a decision based on published access times for both services at different times and for varying file sizes. To make your decision, you purchase a statistical study, which indicates that average download time for Pie in the Sky is 0.77 sec. per MB and for Cloudy but Steady Skies is 0.84. Assume that n1 = n2 = 50, σ1 = 0.2 and σ2 = 0.3. With = .05, the appropriate decision is ______.
a) reject the null hypothesis σ12 < σ22
b) accept the alternate hypothesis μ1 − 2
c) reject the alternate hypothesis n1 = n2 = 50
d) fail to reject the null hypothesis μ1 − μ2 ≤ 0
e) do nothing
Response: See section 10.1 Hypothesis Testing and Confidence Intervals about the Difference in Two Means using the z Statistic (Population Variances Known)
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 10.1: Test hypotheses and develop confidence intervals about the difference in two means with known population variances using the z statistic.
87. You are interested in determining whether the mean price of electricity offered by solar companies is different in the southern states than in the northern states. You select a random sample of 8 solar companies from the southern states and 11 from the northern states. For the southern states, the average price is 12.2 cents per kWh (kilowatt hour) and the standard deviation is 0.8 cents per kWh. For the northern states, the average and standard deviation are 11.7 and 1.0 cents per kWh respectively. If you use a significance level α = 0.10 and assuming the values are normally distributed in both populations, the critical t value from the table is ______.
a) 1.330
b) 1.729
c) 1.734
d) 1.740
e) 1.747
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 10.2: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.
88. You are interested in determining the difference in two population means. You select a random sample of 8 items from the first population and 8 from the second population and then compute a 95% confidence interval. The sample from the first population has an average of 12.2 and a standard deviation of 0.8. The sample from the second population has an average of 11.7 and a standard deviation of 1.0. Assume that the values are normally distributed in each population. The point estimate for the difference in means of these two populations is ______.
a) −0.2
b) 0.2
c) 0.5
d) −0.5
e) 0.06
Difficulty: Easy
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 10.2: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.
89. You are interested in determining the difference in two population means. You select a random sample of 8 items from the first population and 8 from the second population and then compute a 95% confidence interval. The sample from the first population has an average of 12.2 and a standard deviation of 0.8. The sample from the second population has an average of 11.7 and a standard deviation of 1.0. Assume that the values are normally distributed in each population and that the population variances are approximately equal. The corresponding critical t value from the table is ______.
a) 1.753
b) 1.761
c) 2.120
d) 2.131
e) 2.145
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 10.2: Test hypotheses and develop confidence intervals about the difference in two means of independent samples with unknown population variances using the t test.
90. You are evaluating investing in a cognitive training company. For this reason, you want to determine whether users who complete at least 75% of the recommended daily training for two months show improved levels of reading comprehension and problem-solving skills. You select a random sample of new users and get test scores for each participant in the sample. The test score is a composite of reading comprehension and problem-solving skills. Two months later, you randomly select 15 users from the original sample who have completed 75% or more of the recommended training in the last two months and have them take a test similar to the initial test. You are interested in determining whether the average test score before training is different than the average test score after training for this sample. The after-training average is 92.8, which is 2.7 points higher than the before-training average. The sample standard deviation of the differences is 1.2. You can assume that the differences are normally distributed in the population. The degrees of freedom for this test are ______.
a) 30
b) 29
c) 28
d) 15
e) 14
Response: See section 10.3 Statistical Inferences for Two Related Populations
Difficulty: Easy
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 10.3: Test hypotheses and develop confidence intervals about the difference in two dependent populations.
91. You are evaluating investing in a cognitive training company. For this reason, you want to determine whether users who complete at least 75% of the recommended daily training for two months show improved levels of reading comprehension and problem-solving skills. You select a random sample of new users and get test scores for each participant in the sample. The test score is a composite of reading comprehension and problem-solving skills. Two months later, you randomly select 15 users from the original sample who have completed 75% or more of the recommended training in the last two months and have them take a test similar to the initial test. You are interested in determining whether the average test score before training is different than the average test score after training for this sample. The after-training average is 92.8, which is 2.7 points higher than the before-training average. The sample standard deviation of the differences is 1.2. You can assume that the differences are normally distributed in the population. The observed t value for this test is ______.
a) 7.26
b) 8.71
c) 9.55
d) 9.81
e) 33.75
Response: See section 10.3 Statistical Inferences for Two Related Populations
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 10.3: Test hypotheses and develop confidence intervals about the difference in two dependent populations.
92. You are evaluating investing in a cognitive training company. For this reason, you want to determine whether users who complete at least 75% of the recommended daily training for two months show improved levels of reading comprehension and problem-solving skills. You select a random sample of new users and get test scores for each participant in the sample. The test score is a composite of reading comprehension and problem-solving skills. Two months later, you randomly select 15 users from the original sample who have completed 75% or more of the recommended training in the last two months and have them take a test similar to the initial test. You are interested in determining whether the average test score before training is different than the average test score after training for this sample. The after-training average is 92.8, which is 2.7 points higher than the before-training average. The sample standard deviation of the differences is 1.2. You use a significance level of 0.10, and you can assume that the differences are normally distributed in the population. The t-value from the table for this test is ______.
a) 1.761
b) 1.746
c) 1.753
d) 1.345
e) 1.339
Response: See section 10.3 Statistical Inferences for Two Related Populations
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 10.3: Test hypotheses and develop confidence intervals about the difference in two dependent populations.
93. Suppose that the proportion of young adults who read at least one book per month is 0.15, and this proportion is the same in Boston and New York. Suppose that samples of 400 are randomly drawn from each city. The standard deviation of the differences for the sampling distribution between the first sample proportion and the second sample proportion (used to calculate the z score) is _______.
a) 0.0459
b) 0.0435
c) 0.0402
d) 0.0335
e) 0.0252
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 – p2
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
94. Maxwell Cantor, VP of human resources of Asimov Aerospace Industries Inc., is reviewing the technical certifications of employees in different divisions of the company. His goal is to have at least 90% of technical employees with up-to-date certifications. The north-east division typically has maintained higher rates of up-to-date certifications than the southern division. He selects a random sample of 250 employees from the north-east division and 300 from the southern division and finds out that the number of employees with up-to-date certifications are 230 in the north-east division and 265 in the southern division. Maxwell’s null hypothesis is ______.
a) μ1 − μ2 = 0
b) p1 − p2 > 0
c) μ1 − μ2 < 0
d) μ1 − μ2 ≥ 0
e) p1 − p2 ≤ 0
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 − p2
Difficulty: Easy
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
95. Maxwell Cantor, VP of human resources of Asimov Aerospace Industries Inc., is reviewing the technical certifications of employees in different divisions of the company. His goal is to have at least 90% of technical employees with up-to-date certifications. The north-east division typically has maintained higher rates of up-to-date certifications than the southern division. He selects a random sample of 250 employees from the north-east division and 300 from the southern division and finds out that the number of employees with up-to-date certifications are 230 in the north-east division and 265 in the southern division. Maxwell’s alternative hypothesis is ______.
a) μ1 − μ2 = 0
b) p1 − p2 > 0
c) μ1 − μ2 < 0
d) μ1 − μ2 > 0
e) p1 − p2 = 0
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 − p2
Difficulty: Easy
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
96. Maxwell Cantor, VP of human resources of Asimov Aerospace Industries Inc., is reviewing the technical certifications of employees in different divisions of the company. His goal is to have at least 90% of technical employees with up-to-date certifications. The north-east division typically has maintained higher rates of up-to-date certifications than the southern division. He selects a random sample of 250 employees from the north-east division and 300 from the southern division and finds out that the number of employees with up-to-date certifications are 230 in the north-east division and 265 in the southern division. Assuming = 0.01, the critical z value is ______.
a) −2.33
b) 1.645
c) 1.96
d) 2.33
e) 2.576
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 − p2
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
97. Maxwell Cantor, VP of human resources of Asimov Aerospace Industries Inc., is reviewing the technical certifications of employees in different divisions of the company. His goal is to have at least 90% of technical employees with up-to-date certifications. The north-east division typically has maintained higher rates of up-to-date certifications than the southern division. He selects a random sample of 250 employees from the north-east division and 300 from the southern division and finds out that the number of employees with up-to-date certifications are 230 in the north-east division and 265 in the southern division. Assuming = 0.01, the observed z value is ______.
a) 1.027
b) 1.219
c) 1.427
d) 1.619
e) 1.827
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 − p2
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
98. Maxwell Cantor, VP of human resources of Asimov Aerospace Industries Inc., is reviewing the technical certifications of employees in different divisions of the company. His goal is to have at least 90% of technical employees with up-to-date certifications. The north-east division typically has maintained higher rates of up-to-date certifications than the southern division. He selects a random sample of 250 employees from the north-east division and 300 from the southern division and finds out that the number of employees with up-to-date certifications are 230 in the north-east division and 265 in the southern division. Assuming = 0.01, 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
Response: See section 10.4 Statistical Inferences about Two Population Proportions p1 − p2
Difficulty: Hard
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 10.4: Test hypotheses and develop confidence intervals about the difference in two population proportions.
99. Suppose that you can purchase a specialized electronic component from two providers. The electrical resistance of this component needs to be 0.15 ohms (Ω). Both providers offer components with a mean resistance of 0.15 Ω. You are interested in comparing the consistencies of both providers. To this end, you randomly select 15 components from the first provider and 18 from the second one. You can assume that the resistance is approximately normally distributed in the population. If you use a significance level of 0.10, the critical F value from the table for this test is ______.
a) 1.93
b) 2.27
c) 2.33
d) 2.40
e) 2.57
Response: See section 10.5 Testing Hypotheses about Two Population Variances
Difficulty: Medium
AACSB: Reflective thinking
Bloom’s level: Application
Learning Objective: 10.5: Test hypotheses about the difference in two population variances using the F distribution.
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