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Homework answers / question archive / 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
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.
2. The difference in two sample means is normally distributed for sample sizes ≥ 30, only if the populations are normally distributed.
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.
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.
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.
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 010 level of significance.
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.
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.
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.
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.
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.
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.
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.
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.
15. Sets of matched samples are also referred to as independent samples.
16. Sets of matched samples are also referred to as dependent samples.
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.
18. The F test of two population variances is extremely robust to the violations of the assumption that the populations are normally distributed.
Multiple Choice
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) s12 < s22
b) m1- m2 > 0
c) p1 – p2 = 0
d) m1 - m2 = 0
e) s1 – s2 = 0
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) s12 < s22
b) m1- m2 > 0
c) p1 – p2 = 0
d) m1 - m2 = 0
e) s1 – s2 > 0
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 s1 = 2 and s2 = 3. With a = .01, the critical z value is _________________.
a) -1.96
b) 1.96
c) -2.33
d) -1.33
e) 2.33
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 s1 = 2 and s2 = 3. With a = .01, the observed z value is _________________.
a) 2.22
b) 12.81
c) 4.92
d) 3.58
e) 1.96
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 s1 = 2 and s2 = 3. With a = .01, the appropriate decision is _________________.
a) reject the null hypothesis s12 < s22
b) accept the alternate hypothesis m1- m2 > 0
c) reject the alternate hypothesis n1 = n2 = 64
d) fail to reject the null hypothesis m1 - m2 = 0
e) do nothing
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 s1 = 4 and s2 = 3. With a = .01, the observed z value is _________________.
a) 18.29
b) 6.05
c) 5.12
d) 3.40
e) 3.20
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 s1 = 4 and s2 = 3. With a = .01, the appropriate decision is _____________.
a) do nothing
b) reject the null hypothesis s1 < s2
c) accept the alternate hypothesis m1- m2 > 0
d) reject the alternate hypothesis n1 = n2 = 64
e) do not reject the null hypothesis m1 - m2 = 0
26. Lucy Baker is analyzing demographic characteristics of two television programs, COPS (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) m1 - m2 ¹ 0
b) m1 - m2 > 0
c) m1 - m2 = 0
d) m1 - m2 < 0
e) m1 - m2 < 1
27. Lucy Baker is analyzing demographic characteristics of two television programs, COPS (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) m1 - m2 < 0
b) m1 - m2 > 0
c) m1 - m2 = 0
d) m1 - m2 ¹ 0
e) m1 - m2 = 1
28. Lucy Baker is analyzing demographic characteristics of two television programs, COPS (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 s1 = 5 and s2 = 8. With a two-tail test and a = .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
29. Lucy Baker is analyzing demographic characteristics of two television programs, COPS (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 s1 = 5 and s2 = 8. Assuming a two-tail test and a = .05, the observed z value is _________________.
a) -2.12
b) -2.25
c) -5.58
d) -15.38
e) -20.68
30. Lucy Baker is analyzing demographic characteristics of two television programs, COPS (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 s1 = 5 and s2 = 8. With a two-tail test and a = .05, the appropriate decision is _________________.
a) do not reject the null hypothesis m1 - m2 = 0
b) reject the null hypothesis m1 - m2 > 0
c) reject the null hypothesis m1 - m2 = 0
d) do not reject the null hypothesis m1 - m2 < 0
e) do nothing
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
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
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
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
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
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
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
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
39. 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 (s) is _______.
a) 1.3
b) 1.14
c) 1.04
d) 1.02
e) 1.47
40. 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
41. 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
42. 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
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:
|
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
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:
|
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
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:
|
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
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) m1 - m2 = 0
c) p1 – p2 > 0
d) m1 - m2 < 0
e) m1 - m2 ≥ 0
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 ¹ 0
b) m1 - m2 > 0
c) p1 – p2 > 0
d) m1 - m2 ¹ 0
e) m1 - m2 ≥ 0
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 a = 0.05, the critical z value is ___________________.
a) -1.96
b) -1.64
c) 1.64
d) 1.96
e) 2.33
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 a = 0.05, the observed z value is ___________________.
a) -3.15
b) 2.42
c) 1.53
d) 0.95
e) 1.08
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 a = 0.05, the appropriate decision is ___________________.
a) do not reject the null hypothesis m1 - m2 = 0
b) do not reject the null hypothesis p1 – p2 = 0
c) reject the null hypothesis m1 - m2 = 0
d) reject the null hypothesis p1 – p2 = 0
e) do not reject the null hypothesis p1 – p2 ≥ 0
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 a = 0.05, the observed z value is ___________________.
a) -3.15
b) 2.42
c) 1.53
d) 0.95
e) 1.05
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 a = 0.05, the appropriate decision is ___________________.
a) reject the null hypothesis p1 – p2 = 0
b) reject the null hypothesis m1 - m2 < 0
c) do not reject the null hypothesis m1 - m2 = 0
d) do not reject the null hypothesis p1 – p2 = 0
e) do not reject the null hypothesis p1 – p2 ≥ 0
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
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
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
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
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
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
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
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 it 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) s12 = s22
b) s12 ¹ s22
c) s12 > s22
d) s12 < s22
e) s12 < s22
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 it 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) s12 = s22
b) s12 ¹ s22
c) s12 > s22
d) s12 < s22
e) s12 < s22
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 it 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 a = 0.05, the critical F value is _____________.
a) 3.68
b) 3.29
c) 3.50
d) 3.79
e) 3.99
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 it 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 a = 0.05, the observed F value is ___________.
a) 0.50
b) 2.00
c) 1.41
d) 0.91
e) 0.71
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 it 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 a = 0.05, the appropriate decision is ________.
a) reject the null hypothesis s12 = s22
b) reject the null hypothesis s12 < s22
c) do not reject the null hypothesis s12 = s22
d) do not reject the null hypothesis s12 < s22
e) do nothing
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 it 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 a = 0.05, the observed F value is ___________.
a) 0.27
b) 0.52
c) 1.92
d) 3.75
e) 4.25
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 it 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 a = 0.05, the appropriate decision is _________.
a) reject the null hypothesis s12 = s22
b) reject the null hypothesis s12 < s22
c) do not reject the null hypothesis s12 = s22
d) do not reject the null hypothesis s12 < s22
e) do nothing
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 a = 0.05, Tamara's null hypothesis is _______.
a) s12 = s22
b) s12 ¹ s22
c) s12 > s22
d) s12 < s22
e) s12 < s22
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 a = 0.05, Tamara's alternate hypothesis is _______.
a) s12 = s22
b) s12 ¹ s22
c) s12 > s22
d) s12 < s22
e) s12 < s22
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 a = 0.05, the critical F value is _______.
a) 3.68
b) 3.58
c) 4.15
d) 3.29
e) 4.89
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 a = 0.05, the observed F value is _______.
a) 3.13
b) 0.32
c) 1.77
d) 9.77
e) 9.87
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 a = 0.05, the appropriate decision is _______.
a) reject the null hypothesis s12 = s22
b) reject the null hypothesis s12 ¹ s22
c) do not reject the null hypothesis s12 = s22
d) do not reject the null hypothesis s12 ¹ s22
e) do nothing
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 a = 0.05, the observed F value is _______.
a) 17.36
b) 2.04
c) 0.24
d) 4.77
e) 4.17
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 a = 0.05, the appropriate decision is _______.
a) reject the null hypothesis s12 = s22
b) reject the null hypothesis s12 ¹ s22
c) do not reject the null hypothesis s12 = s22
d) do not reject the null hypothesis s12 ¹ s22
e) maintain status quo
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