Chapter 10

a. normal distribution

10. The sampling distribution of pbar1-pbar2 is approximated by a a. normal distribution b. t-distribution with n1 + n2 degrees of freedom c. t-distribution with n1 + n2 - 1 degrees of freedom d. t-distribution with n1 + n2 + 2 degrees of freedom

b. is not restricted to small sample situations

2. To compute an interval estimate for the difference between the means of two populations, the t distribution a. is restricted to small sample situations b. is not restricted to small sample situations c. can be applied when the populations have equal means d. None of these alternatives is correct.

d. n1 and n2 can be of different sizes,

3. When developing an interval estimate for the difference between two sample means, with sample sizes of n1 and n2, a. n1 must be equal to n2 b. n1 must be smaller than n2 c. n1 must be larger than n2 d. n1 and n2 can be of different sizes,

c. (n1 + n2 - 2) degrees of freedom

4. To construct an interval estimate for the difference between the means of two populations when the standard deviations of the two populations are unknown and it can be assumed the two populations have equal variances, we must use a t distribution with (let n1 be the size of sample 1 and n2 the size of sample 2) a. (n1 + n2) degrees of freedom b. (n1 + n2 - 1) degrees of freedom c. (n1 + n2 - 2) degrees of freedom d. n1 - n2 + 2

d. 3.01

41. Refer to Exhibit 10-8. The test statistic is a. 0.098 b. 1.645 c. 2.75 d. 3.01

b. 0.0026

42. Refer to Exhibit 10-8. The p-value is a. 0.0013 b. 0.0026 c. 0.0042 d. 0.0084

a. should be rejected

43. Refer to Exhibit 10-8. The null hypothesis a. should be rejected b. should not be rejected c. should be revised d. None of these alternatives is correct.

c. alternative hypothesis should state P1 - P2 > 0

1. If we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in population 2, the a. null hypothesis should state P1 - P2 < 0 b. null hypothesis should state P1 - P2 ≥ 0 c. alternative hypothesis should state P1 - P2 > 0 d. alternative hypothesis should state P1 - P2 < 0

c. 0.0225

48. Refer to Exhibit 10-10. The standard error of pbar1-pbar2 is a. 52 b. 0.044 c. 0.0225 d. 100

b. 0.044

49. Refer to Exhibit 10-10. At 95% confidence, the margin of error is a. 0.064 b. 0.044 c. 0.0225 d. 52

b. matched samples

5. When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as a. corresponding samples b. matched samples c. independent samples d. None of these alternatives is correct.

a. -0.024 to 0.064

50. Refer to Exhibit 10-10. The 95% confidence interval estimate for the difference between the populations favoring the products is a. -0.024 to 0.064 b. 0.6 to 0.7 c. 0.024 to 0.7 d. 0.02 to 0.3

d. 0.0243

56. Refer to Exhibit 10-12. The standard error of is a. 0.48 b. 0.50 c. 0.03 d. 0.0243

d. -0.068 to 0.028

57. Refer to Exhibit 10-12. The 95% confidence interval for the difference between the two proportions is a. 384 to 450 b. 0.48 to 0.5 c. 0.028 to 0.068 d. -0.068 to 0.028

b. 0.8

59. Refer to Exhibit 10-13. The point estimate of the difference between the means is a. 20 b. 0.8 c. 0.50 d. -20

d. t distribution with 70 degrees of freedom

6. Independent simple random samples are taken to test the difference between the means of two populations whose variances are not known, but are assumed to be equal. The sample sizes are n1 = 32 and n2 = 40. The correct distribution to use is the a. t distribution with 73 degrees of freedom b. t distribution with 72 degrees of freedom c. t distribution with 71 degrees of freedom d. t distribution with 70 degrees of freedom

d. 2.7

60. Refer to Exhibit 10-13. The test statistic has a value of a. 1.96 b. 1.645 c. 0.80 d. 2.7

b. 0.007

61. Refer to Exhibit 10-13. The p-value is a. 0.0035 b. 0.007 c. 0.4965 d. 1.96

d. t distribution with 58 degrees of freedom

7. Independent simple random samples are taken to test the difference between the means of two populations whose standard deviations are not known, but are assumed to be equal. The sample sizes are n1 = 25 and n2 = 35. The correct distribution to use is the a. t distribution with 61 degrees of freedom b. t distribution with 60 degrees of freedom c. t distribution with 59 degrees of freedom d. t distribution with 58 degrees of freedom

c. can be approximated by a normal

8. If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample means a. can be approximated by a Poisson distribution b. will have a variance of one c. can be approximated by a normal distribution d. will have a mean of one

c. standard deviation of the sampling distribution of xbar1-xbar2

9. The standard error of xbar1- xbar2 is the a. variance of xbar1-xbar2 b. variance of the sampling distribution of xbar1-xbar2 c. standard deviation of the sampling distribution of xbar1-xbar2 d. difference between the two means

b. 3

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary (in $1,000) 44 41 Population Variance (σ2) 128 72 11. Refer to Exhibit 10-1. The point estimate of the difference between the means of the two populations is a. -28 b. 3 c. 4 d. -4

d. 2.0

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary (in $1,000) 44 41 Population Variance (σ2) 128 72 12. Refer to Exhibit 10-1. The standard error for the difference between the two means is a. 4 b. 7.46 c. 4.24 d. 2.0

c. 3.920

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary (in $1,000) 44 41 Population Variance (σ2) 128 72 13. Refer to Exhibit 10-1. At 95% confidence, the margin of error is a. 1.96 b. 1.645 c. 3.920 d. 2.000

d. -0.92 to 6.92

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary (in $1,000) 44 41 Population Variance (σ2) 128 72 14. Refer to Exhibit 10-1. The 95% confidence interval for the difference between the means of the two populations is a. 0 to 6.92 b. -2 to 2 c. -1.96 to 1.96 d. -0.92 to 6.92

b. 1.5

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary (in $1,000) 44 41 Population Variance (σ2) 128 72 15. Refer to Exhibit 10-1. If you are interested in testing whether or not the average salary of males is significantly greater than that of females, the test statistic is a. 2.0 b. 1.5 c. 1.96 d. 1.645

a. 0.0668

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary (in $1,000) 44 41 Population Variance (σ2) 128 72 16. Refer to Exhibit 10-1. The p-value is a. 0.0668 b. 0.0334 c. 1.336 d. 1.96

d. 0.02

Exhibit 10-10 The results of a recent poll on the preference of shoppers regarding two products are shown below. Product Shoppers Surveyed Shoppers Favoring This Product A 800 560 B 900 612 47. Refer to Exhibit 10-10. The point estimate for the difference between the two population proportions in favor of this product is a. 52 b. 100 c. 0.44 d. 0.02

d. 3.96

Exhibit 10-11 An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Under Age of 18 Over Age of 18 n1 = 500 n2 = 600 Number of accidents = 180 Number of accidents = 150 53. Refer to Exhibit 10-11. The test statistic is a. 0.96 b. 1.96 c. 2.96 d. 3.96

a. less than 0.001

Exhibit 10-11 An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Under Age of 18 Over Age of 18 n1 = 500 n2 = 600 Number of accidents = 180 Number of accidents = 150 54. Refer to Exhibit 10-11. The p-value is a. less than 0.001 b. more than 0.10 c. 0.0228 d. 0.3

d. pu - po = 0

Exhibit 10-11 An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Under Age of 18 Over Age of 18 n1 = 500 n2 = 600 Number of accidents = 180 Number of accidents = 150 We are interested in determining if the accident proportions differ between the two age groups. 51. Refer to Exhibit 10-11 and let pu represent the proportion under and po the proportion over the age of 18. The null hypothesis is a. pu - po ≤ 0 b. pu - po ≥ 0 c. pu - po ≠ 0 d. pu - po = 0

b. 0.300

Exhibit 10-11 An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below. Under Age of 18 Over Age of 18 n1 = 500 n2 = 600 Number of accidents = 180 Number of accidents = 150 52. Refer to Exhibit 10-11. The pooled proportion is a. 0.305 b. 0.300 c. 0.027 d. 0.450

a. -0.02

Exhibit 10-12 The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below. Music Type Teenagers Surveyed Teenagers Favoring This Type Pop 800 384 Rap 900 450 55. Refer to Exhibit 10-12. The point estimate for the difference between the proportions is a. -0.02 b. 0.048 c. 100 d. 66

d. μ1 - μ2 = 0

Exhibit 10-13 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company 1 Company 2 n1 = 80 n2 = 60 x1= $10.80 x2 = $10.00 std dev = $2.00 std dev = $1.50 58. Refer to Exhibit 10-13. The null hypothesis for this test is a. μ1 - μ2 ≠ 0 b. μ1 - μ2 >= 0 c. μ1 - μ2 <= 0 d. μ1 - μ2 = 0

c. 0

Exhibit 10-2 The following information was obtained from matched samples. The daily production rates for a sample of workers before and after a training program are shown below. Worker Before After 1 20 22 2 25 23 3 27 27 4 23 20 5 22 25 6 20 19 7 17 18 19. Refer to Exhibit 10-2. The null hypothesis to be tested is H0: μd = 0. The test statistic is a. -1.96 b. 1.96 c. 0 d. 1.645

b. null hypothesis should not be rejected

Exhibit 10-2 The following information was obtained from matched samples. The daily production rates for a sample of workers before and after a training program are shown below. Worker Before After 1 20 22 2 25 23 3 27 27 4 23 20 5 22 25 6 20 19 7 17 18 20. Refer to Exhibit 10-2. Based on the results of question 18, the a. null hypothesis should be rejected b. null hypothesis should not be rejected c. alternative hypothesis should be accepted d. None of these alternatives is correct.

c. 0

Exhibit 10-2 The following information was obtained from matched samples. The daily production rates for a sample of workers before and after a training program are shown below. Worker Before After 1 20 22 2 25 23 3 27 27 4 23 20 5 22 25 6 20 19 7 17 18 18. Refer to Exhibit 10-2. The point estimate for the difference between the means of the two populations is a. -1 b. -2 c. 0 d. 1

d. -6

Exhibit 10-3 A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. Today Five Years Ago 82 88 σ2 112.5 54 n 45 36 21. Refer to Exhibit 10-3. The point estimate for the difference between the means of the two populations is a. 58.5 b. 9 c. -9 d. -6

d. 2

Exhibit 10-3 A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. Today Five Years Ago 82 88 σ2 112.5 54 n 45 36 22. Refer to Exhibit 10-3. The standard error of is a. 12.9 b. 9.3 c. 4 d. 2

c. 20

Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. Sample 1 Sample 2 Sample Mean 45 42 Sample Variance 85 90 Sample Size 10 12 29. Refer to Exhibit 10-4. The degrees of freedom for the t-distribution are a. 22 b. 21 c. 20 d. 19

a. -9.92 to -2.08

Exhibit 10-3 A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. Today Five Years Ago 82 88 σ2 112.5 54 n 45 36 23. Refer to Exhibit 10-3. The 95% confidence interval for the difference between the two population means is a. -9.92 to -2.08 b. -3.92 to 3.92 c. -13.84 to 1.84 d. -24.228 to 12.23

d. -3

Exhibit 10-3 A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. Today Five Years Ago 82 88 σ2 112.5 54 n 45 36 24. Refer to Exhibit 10-3. The test statistic for the difference between the two population means is a. -.47 b. -.65 c. -1.5 d. -3

b. .0026

Exhibit 10-3 A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. Today Five Years Ago 82 88 σ2 112.5 54 n 45 36 25. Refer to Exhibit 10-3. The p-value for the difference between the two population means is a. .0013 b. .0026 c. .4987 d. .9987

a. There is a statistically significant difference in the average final examination scores between the two classes.

Exhibit 10-3 A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. Today Five Years Ago 82 88 σ2 112.5 54 n 45 36 26. Refer to Exhibit 10-3. What is the conclusion that can be reached about the difference in the average final examination scores between the two classes? (Use a .05 level of significance.) a. There is a statistically significant difference in the average final examination scores between the two classes. b. There is no statistically significant difference in the average final examination scores between the two classes. c. It is impossible to make a decision on the basis of the information given. d. There is a difference, but it is not significant.

c. 3

Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. Sample 1 Sample 2 Sample Mean 45 42 Sample Variance 85 90 Sample Size 10 12 27. Refer to Exhibit 10-4. The point estimate for the difference between the means of the two populations is a. 0 b. 2 c. 3 d. 15

b. 4.0

Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. Sample 1 Sample 2 Sample Mean 45 42 Sample Variance 85 90 Sample Size 10 12 28. Refer to Exhibit 10-4. The standard error of xbar1-xbar2 is a. 3.0 b. 4.0 c. 8.372 d. 19.48

a. -5.372 to 11.372

Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. Sample 1 Sample 2 Sample Mean 45 42 Sample Variance 85 90 Sample Size 10 12 30. Refer to Exhibit 10-4. The 95% confidence interval for the difference between the two population means is a. -5.372 to 11.372 b. -5 to 3 c. -4.86 to 10.86 d. -2.65 to 8.65

b. should not be rejected

Exhibit 10-5 The following information was obtained from matched samples. Individual Method 1 Method 2 1 7 5 2 5 9 3 6 8 4 7 7 5 5 6 34. Refer to Exhibit 10-5. If the null hypothesis is tested at the 5% level, the null hypothesis a. should be rejected b. should not be rejected c. should be revised d. None of these alternatives is correct.

a. -1

Exhibit 10-5 The following information was obtained from matched samples. Individual Method 1 Method 2 1 7 5 2 5 9 3 6 8 4 7 7 5 5 6 31. Refer to Exhibit 10-5. The point estimate for the difference between the means of the two populations (Method 1 - Method 2) is a. -1 b. 0 c. -4 d. 2

a. -3.776 to 1.776

Exhibit 10-5 The following information was obtained from matched samples. Individual Method 1 Method 2 1 7 5 2 5 9 3 6 8 4 7 7 5 5 6 32. Refer to Exhibit 10-5. The 95% confidence interval for the difference between the two population means is a. -3.776 to 1.776 b. -2.776 to 2.776 c. -1.776 to 2.776 d. 0 to 3.776

c. -1

Exhibit 10-5 The following information was obtained from matched samples. Individual Method 1 Method 2 1 7 5 2 5 9 3 6 8 4 7 7 5 5 6 33. Refer to Exhibit 10-5. The null hypothesis tested is H0: μd = 0. The test statistic for the difference between the two population means is a. 2 b. 0 c. -1 d. -2

d. 15

Exhibit 10-6 The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information. Store's Card Major Credit Card Sample size 64 49 Sample mean $140 $125 Population standard deviation $10 $8 35. Refer to Exhibit 10-6. A point estimate for the difference between the mean purchases of the users of the two credit cards is a. 2 b. 18 c. 265 d. 15

b. 3.32

Exhibit 10-6 The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information. Store's Card Major Credit Card Sample size 64 49 Sample mean $140 $125 Population standard deviation $10 $8 36. Refer to Exhibit 10-6. At 95% confidence, the margin of error is a. 1.694 b. 3.32 c. 1.96 d. 15

b. 11.68 to 18.32

Exhibit 10-6 The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information. Store's Card Major Credit Card Sample size 64 49 Sample mean $140 $125 Population standard deviation $10 $8 37. Refer to Exhibit 10-6. A 95% confidence interval estimate for the difference between the average purchases of the customers using the two different credit cards is a. 49 to 64 b. 11.68 to 18.32 c. 125 to 140 d. 8 to 10

a. 1

Exhibit 10-7 In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered. Downtown Store North Mall Store Sample size 25 20 Sample mean $9 $8 Sample standard deviation $2 $1 38. Refer to Exhibit 10-7. A point estimate for the difference between the two sample means is a. 1 b. 2 c. 3 d. 4

a. 0.078 to 1.922

Exhibit 10-7 In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered. Downtown Store North Mall Store Sample size 25 20 Sample mean $9 $8 Sample standard deviation $2 $1 39. Refer to Exhibit 10-7. A 95% interval estimate for the difference between the two population means is a. 0.078 to 1.922 b. 1.922 to 2.078 c. 1.09 to 4.078 d. 1.078 to 2.922

b. 0.50

Exhibit 10-8 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company A Company B Sample size 80 60 Sample mean $16.75 $16.25 Population standard deviation $1.00 $0.95 40. Refer to Exhibit 10-8. A point estimate for the difference between the two sample means is a. 20 b. 0.50 c. 0.25 d. 1.00

c. 2.0

Exhibit 10-9 Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test. Driver Manufacturer A Manufacturer B 1 32 28 2 27 22 3 26 27 4 26 24 5 25 24 6 29 25 7 31 28 8 25 27 44. Refer to Exhibit 10-9. The mean for the differences is a. 0.50 b. 1.5 c. 2.0 d. 2.5

d. 2.256

Exhibit 10-9 Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test. Driver Manufacturer A Manufacturer B 1 32 28 2 27 22 3 26 27 4 26 24 5 25 24 6 29 25 7 31 28 8 25 27 45. Refer to Exhibit 10-9. The test statistic is a. 1.645 b. 1.96 c. 2.096 d. 2.256

...

Exhibit 10-9 Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test. Driver Manufacturer A Manufacturer B 1 32 28 2 27 22 3 26 27 4 26 24 5 25 24 6 29 25 7 31 28 8 25 27 46. Refer to Exhibit 10-9. At 90% confidence the null hypothesis a. should not be rejected b. should be rejected c. should be revised d. None of these alternatives is correct.

d. None of these alternatives is correct.

Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary (in $1,000) 44 41 Population Variance (σ2) 128 72 17. Refer to Exhibit 10-1. At 95% confidence, the conclusion is the a. average salary of males is significantly greater than females b. average salary of males is significantly lower than females c. salaries of males and females are equal d. None of these alternatives is correct.