IS310 Chapter 9

41. For a two-tailed test at 86.12% confidence, Z = a. 1.96 b. 1.48 c. 1.09 d. 0.86

b. 1.48

49. For a one-tailed test (lower tail) at 89.8% confidence, Z = a. -1.27 b. -1.53 c. -1.96 d. -1.64

a. -1.27

51. For a one-tailed test (upper tail), a sample size of 26 at 90% confidence, t = a. 1.316 b. -1.316 c. -1.740 d. 1.740

a. 1.316

44. For a two-tailed test, a sample of 20 at 80% confidence, t = a. 1.328 b. 2.539 c. 1.325 d. 2.528

a. 1.328

Exhibit 9-1 n = 36 = 24.6 S = 12 H0: μ 20 Ha: μ > 20 56. Refer to Exhibit 9-1. The test statistic is a. 2.3 b. 0.38 c. -2.3 d. -0.38

a. 2.3

23. In order to test the following hypotheses at an α level of significance H0: μ <= 100 Ha: μ > 100 the null hypothesis will be rejected if the test statistic Z is a. > = Zα b. < = Zα c. < -Zα d. < 100

a. > = Zα

28. A weatherman stated that the average temperature during July in Chattanooga is less than 80 degrees. A sample of 32 Julys is taken. The correct set of hypotheses is a. H0: μ >= 80 Ha: μ < 80 b. H0: μ <= 80 Ha: μ > 80 c. H0: μ ≠ 80 Ha: μ = 80 d. H0: μ < 80 Ha: μ > 80

a. H0: μ >= 80 Ha: μ < 80

2. What type of error occurs if you fail to reject H0 when, in fact, it is not true? a. Type II b. Type I c. either Type I or Type II, depending on the level of significance d. either Type I or Type II, depending on whether the test is one tail or two tail

a. Type II

15. The error of rejecting a true null hypothesis is a. a Type I error b. a Type II error c. is the same as Beta d. committed when not enough information is available

a. a Type I error

14. A Type II error is committed when a. a true alternative hypothesis is mistakenly rejected b. a true null hypothesis is mistakenly rejected c. the sample size has been too small d. not enough information has been available

a. a true alternative hypothesis is mistakenly rejected

7. For a lower tail test, the p-value is the probability of obtaining a value for the test statistic a. at least as small as that provided by the sample b. at least as large as that provided by the sample c. at least as small as that provided by the population d. at least as large as that provided by the population.

a. at least as small as that provided by the sample

3. An assumption made about the value of a population parameter is called a a. hypothesis b. conclusion c. confidence d. significance

a. hypothesis

Exhibit 9-3 n = 49 = 54.8 s = 28 H0: μ 50 Ha: μ > 50 64. Refer to Exhibit 9-3. If the test is done at the 5% level of significance, the null hypothesis should a. not be rejected b. be rejected c. Not enough information given to answer this question. d. None of these alternatives is correct.

a. not be rejected

8. The p-value is a probability that measures the support (or lack of support) for the a. null hypothesis b. alternative hypothesis c. either the null or the alternative hypothesis d. sample statistic

a. null hypothesis

22. When the p-value is used for hypothesis testing, the null hypothesis is rejected if a. p-value < = α b. α < p-value c. p-value>= α d. p-value = α

a. p-value < = α

Exhibit 9-4 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. 67. Refer to Exhibit 9-4. At 95% confidence, it can be concluded that the mean of the population is a. significantly greater than 3 b. not significantly greater than 3 c. significantly less than 3 d. significantly greater then 3.18

a. significantly greater than 3

25. In the hypothesis testing procedure, α is a. the level of significance b. the critical value c. the confidence level d. 1 - level of significance

a. the level of significance

37. If a hypothesis is not rejected at the 5% level of significance, it a. will also not be rejected at the 1% level b. will always be rejected at the 1% level c. will sometimes be rejected at the 1% level d. None of these alternatives is correct.

a. will also not be rejected at the 1% level

19. The probability of making a Type I error is denoted by a. α b. β c. 1 - α d. 1 - β

a. α

21. When the following hypotheses are being tested at a level of significance of α H0: μ <= 100 Ha: μ < 100 the null hypothesis will be rejected if the p-value is a. α b. > α c. > α/2 d. α/2

a. α

Exhibit 9-9 The sales of a grocery store had an average of $8,000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8,250 per day. From past information, it is known that the standard deviation of the population is $1,200. 80. Refer to Exhibit 9-9. The correct null hypothesis for this problem is a. μ <= 8000 b. μ >= 8000 c. μ = 8000 d. μ >= 8250

a. μ <= 8000

42. For a one-tailed test (lower tail) at 93.7% confidence, Z = a. -1.86 b. -1.53 c. -1.96 d. -1.645

b. -1.53

Exhibit 9-2 n = 64 = 50 s = 16 H0: μ 54 Ha: μ < 54 60. Refer to Exhibit 9-2. The p-value is between a. .005 to .01 b. .01 to .025 c. .025 to .05 d. .05 to .01

b. .01 to .025

Exhibit 9-4 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. 66. Refer to Exhibit 9-4. The p-value is between a. .005 to .01 b. .01 to .025 c. .025 to .05 d. .05 to .10

b. .01 to .025

Exhibit 9-8 The average gasoline price of one of the major oil companies in Europe has been $1.25 per liter. Recently, the company has undertaken several efficiency measures in order to reduce prices. Management is interested in determining whether their efficiency measures have actually reduced prices. A random sample of 49 of their gas stations is selected and the average price is determined to be $1.20 per liter. Furthermore, assume that the standard deviation of the population (σ) is $0.14. 79. Refer to Exhibit 9-8. The p-value for this problem is a. 0.4938 b. 0.0062 c. 0.0124 d. 0.05

b. 0.0062

Exhibit 9-1 n = 36 = 24.6 S = 12 H0: μ 20 Ha: μ > 20 57. Refer to Exhibit 9-1. The p-value is between a. 0.005 to 0.01 b. 0.01 to 0.025 c. 0.025 to 0.05 d. 0.05 to 0.10

b. 0.01 to 0.025

55. In a one-tailed hypothesis test (lower tail) the test statistic is determined to be -2. The p-value for this test is a. 0.4772 b. 0.0228 c. 0.0056 d. 0.5228

b. 0.0228

38. The probability of rejecting a false null hypothesis is equal to a. 1 - α b. 1 - β c. α d. β

b. 1 - β

Exhibit 9-7 A random sample of 16 statistics examinations from a large population was taken. The average score in the sample was 78.6 with a variance of 64. We are interested in determining whether the average grade of the population is significantly more than 75. Assume the distribution of the population of grades is normal. 74. Refer to Exhibit 9-7. The test statistic is a. 0.45 b. 1.80 c. 3.6 d. 8

b. 1.80

Exhibit 9-6 A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. 71. Refer to Exhibit 9-6. The test statistic is a. 1.96 b. 2.00 c. 1.645 d. 0.05

b. 2.00

30. The school's newspaper reported that the proportion of students majoring in business is more than 30%. You plan on taking a sample to test the newspaper's claim. The correct set of hypotheses is a. H0: P < 0.30 Ha: P >= 0.30 b. H0: P <= 0.30 Ha: P > 0.30 c. H0: P >= 0.30 Ha: P < 0.30 d. H0: P > 0.30 Ha: P <= 0.30

b. H0: P <= 0.30 Ha: P > 0.30

27. Your investment executive claims that the average yearly rate of return on the stocks she recommends is more than 10.0%. You plan on taking a sample to test her claim. The correct set of hypotheses is a. H0: μ < 10.0% Ha: μ >=10.0% b. H0: μ <= 10.0% Ha: μ > 10.0% c. H0: μ > 10.0% Ha: μ <= 10.0% d. H0: μ => 10.0% Ha: μ < 10.0%

b. H0: μ <= 10.0% Ha: μ > 10.0%

32. The average life expectancy of tires produced by the Whitney Tire Company has been 40,000 miles. Management believes that due to a new production process, the life expectancy of their tires has increased. In order to test the validity of their belief, the correct set of hypotheses is a. H0: μ < 40,000 Ha: μ >= 40,000 b. H0: μ <= 40,000 Ha: μ > 40,000 c. H0: μ > 40,000 Ha: μ <= 40,000 d. H0: μ >= 40,000 Ha: μ < 40,000

b. H0: μ <= 40,000 Ha: μ > 40,000

35. The manager of an automobile dealership is considering a new bonus plan in order to increase sales. Currently, the mean sales rate per salesperson is five automobiles per month. The correct set of hypotheses for testing the effect of the bonus plan is a. H0: μ < 5 Ha: μ <= 5 b. H0: μ <= 5 Ha: μ > 5 c. H0: μ > 5 Ha: μ <= 5 d. H0: μ >= 5 Ha: μ < 5

b. H0: μ <= 5 Ha: μ > 5

Exhibit 9-1 n = 36 = 24.6 S = 12 H0: μ 20 Ha: μ > 20 58. Refer to Exhibit 9-1. If the test is done at 95% confidence, the null hypothesis should a. not be rejected b. be rejected c. Not enough information is given to answer this question. d. None of these alternatives is correct.

b. be rejected

Exhibit 9-2 n = 64 = 50 s = 16 H0: μ 54 Ha: μ < 54 61. Refer to Exhibit 9-2. If the test is done at 95% confidence, the null hypothesis should a. not be rejected b. be rejected c. Not enough information is given to answer this question. d. None of these alternatives is correct.

b. be rejected

Exhibit 9-5 A random sample of 100 people was taken. Eighty-five of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%. 70. Refer to Exhibit 9-5. At 95% confidence, it can be concluded that the proportion of the population in favor of candidate A a. is significantly greater than 80% b. is not significantly greater than 80% c. is significantly greater than 85% d. is not significantly greater than 85%

b. is not significantly greater than 80%

Exhibit 9-7 A random sample of 16 statistics examinations from a large population was taken. The average score in the sample was 78.6 with a variance of 64. We are interested in determining whether the average grade of the population is significantly more than 75. Assume the distribution of the population of grades is normal. 76. Refer to Exhibit 9-7. At 95% confidence, it can be concluded that the average grade of the population a. is not significantly greater than 75 b. is significantly greater than 75 c. is not significantly greater than 78.6 d. is significantly greater than 78.6

b. is significantly greater than 75

12. The level of significance is the a. maximum allowable probability of Type II error b. maximum allowable probability of Type I error c. same as the confidence coefficient d. same as the p-value

b. maximum allowable probability of Type I error

47. A two-tailed test is performed at 95% confidence. The p-value is determined to be 0.09. The null hypothesis a. must be rejected b. should not be rejected c. could be rejected, depending on the sample size d. has been designed incorrectly

b. should not be rejected

11. In hypothesis testing if the null hypothesis is rejected, a. no conclusions can be drawn from the test b. the alternative hypothesis is true c. the data must have been accumulated incorrectly d. the sample size has been too small

b. the alternative hypothesis is true

6. In hypothesis testing, the tentative assumption about the population parameter is a. the alternative hypothesis b. the null hypothesis c. either the null or the alternative d. None of these alternatives is correct.

b. the null hypothesis

5. In hypothesis testing, a. the smaller the Type I error, the smaller the Type II error will be b. the smaller the Type I error, the larger the Type II error will be c. Type II error will not be effected by Type I error d. the sum of Type I and Type II errors must equal to 1

b. the smaller the Type I error, the larger the Type II error will be

10. For a two-tail test, the p-value is the probability of obtaining a value for the test statistic as a. likely as that provided by the sample b. unlikely as that provided by the sample c. likely as that provided by the population d. unlikely as that provided by the population

b. unlikely as that provided by the sample

40. If a hypothesis is rejected at 95% confidence, it a. will always be accepted at 90% confidence b. will always be rejected at 90% confidence c. will sometimes be rejected at 90% confidence d. None of these alternatives is correct.

b. will always be rejected at 90% confidence

20. The probability of making a Type II error is denoted by a. α b. β c. 1 - α d. 1 - β

b. β

46. For a one-tailed test (lower tail), a sample size of 10 at 90% confidence, t = a. 1.383 b. 2.821 c. -1.383 d. -2.821

c. -1.383

52. For a one-tailed test (lower tail) with 22 degrees of freedom at 95% confidence, the value of t = a. -1.383 b. 1.383 c. -1.717 d. -1.721

c. -1.717

Exhibit 9-2 n = 64 = 50 s = 16 H0: μ 54 Ha: μ < 54 59. Refer to Exhibit 9-2. The test statistic equals a. -4 b. -3 c. -2 d. -1

c. -2

Exhibit 9-8 The average gasoline price of one of the major oil companies in Europe has been $1.25 per liter. Recently, the company has undertaken several efficiency measures in order to reduce prices. Management is interested in determining whether their efficiency measures have actually reduced prices. A random sample of 49 of their gas stations is selected and the average price is determined to be $1.20 per liter. Furthermore, assume that the standard deviation of the population (σ) is $0.14. 78. Refer to Exhibit 9-8. The value of the test statistic for this hypothesis test is a. 1.96 b. 1.645 c. -2.5 d. -1.645

c. -2.5

A random sample of 16 statistics examinations from a large population was taken. The average score in the sample was 78.6 with a variance of 64. We are interested in determining whether the average grade of the population is significantly more than 75. Assume the distribution of the population of grades is normal. 75. Refer to Exhibit 9-7. The p-value is between a. .005 to .01 b. .01 to .025 c. .025 to .05 d. .05 to 0.1

c. .025 to .05

Exhibit 9-6 A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. 72. Refer to Exhibit 9-6. The p-value is between a. .005 to .01 b. .01 to .025 c. .025 to .05 d. .05 to .10

c. .025 to .05

Exhibit 9-9 The sales of a grocery store had an average of $8,000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8,250 per day. From past information, it is known that the standard deviation of the population is $1,200. 82. Refer to Exhibit 9-9. The p-value is a. 1.67 b. 0.4525 c. 0.0475 d. 0.5475

c. 0.0475

Exhibit 9-5 A random sample of 100 people was taken. Eighty-five of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%. 68. Refer to Exhibit 9-5. The test statistic is a. 0.80 b. 0.05 c. 1.25 d. 2.00

c. 1.25

Exhibit 9-4 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. 65. Refer to Exhibit 9-4. The test statistic is a. 1.96 b. 1.64 c. 2.00 d. 0.056

c. 2.00

48. For a two-tailed test at 98.4% confidence, Z = a. 1.96 b. 1.14 c. 2.41 d. 0.8612

c. 2.41

34. The academic planner of a university thinks that at least 35% of the entire student body attends summer school. The correct set of hypotheses to test his belief is a. H0: P > 0.35 Ha: P >= 0.35 b. H0: P <= 0.35 Ha: P > 0.35 c. H0: P >= 0.35 Ha: P < 0.35 d. H0: P > 0.35 Ha: P <= 0.35

c. H0: P >= 0.35 Ha: P < 0.35

29. A student believes that the average grade on the final examination in statistics is at least 85. She plans on taking a sample to test her belief. The correct set of hypotheses is a. H0: μ < 85 Ha: μ >= 85 b. H0: μ <= 85 Ha: μ > 85 c. H0: μ >= 85 Ha: μ < 85 d. H0: μ > 85 Ha: μ <= 85

c. H0: μ >= 85 Ha: μ < 85

17. The level of significance a. can be any positive value b. can be any value c. is (1 - confidence level) d. can be any value between -1.96 to 1.96

c. is (1 - confidence level)

16. The level of significance in hypothesis testing is the probability of a. accepting a true null hypothesis b. accepting a false null hypothesis c. rejecting a true null hypothesis d. None of these alternatives is correct.

c. rejecting a true null hypothesis

24. Which of the following does not need to be known in order to compute the p-value? a. knowledge of whether the test is one-tailed or two-tailed b. the value of the test statistic c. the level of significance d. None of these alternatives is correct.

c. the level of significance

39. If the level of significance of a hypothesis test is raised from .01 to .05, the probability of a Type II error a. will also increase from .01 to .05 b. will not change c. will decrease d. will increase

c. will decrease

54. In a two-tailed hypothesis test the test statistic is determined to be Z = -2.5. The p-value for this test is a. -1.25 b. 0.4938 c. 0.0062 d. 0.0124

d. 0.0124

Exhibit 9-8 The average gasoline price of one of the major oil companies in Europe has been $1.25 per liter. Recently, the company has undertaken several efficiency measures in order to reduce prices. Management is interested in determining whether their efficiency measures have actually reduced prices. A random sample of 49 of their gas stations is selected and the average price is determined to be $1.20 per liter. Furthermore, assume that the standard deviation of the population (σ) is $0.14. 77. Refer to Exhibit 9-8. The standard error has a value of a. 0.14 b. 7 c. 2.5 d. 0.02

d. 0.02

63. Refer to Exhibit 9-3. n = 49 = 54.8 s = 28 H0: μ 50 Ha: μ > 50 The p-value is between a. 0.01 to 0.025 b. 0.025 to 0.05 c. .05 to 0.1 d. 0.1 to 0.2

d. 0.1 to 0.2

Exhibit 9-5 A random sample of 100 people was taken. Eighty-five of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%. 69. Refer to Exhibit 9-5. The p-value is a. 0.2112 b. 0.05 c. 0.025 d. 0.1056

d. 0.1056

43. Read the Z statistic from the normal distribution table and circle the correct answer. A one-tailed test (upper tail) at 87.7% confidence; Z = a. 1.54 b. 1.96 c. 1.645 d. 1.16

d. 1.16

Exhibit 9-3 n = 49 = 54.8 s = 28 H0: μ 50 Ha: μ > 50 62. Refer to Exhibit 9-3. The test statistic is a. 0.1714 b. 0.3849 c. -1.2 d. 1.2

d. 1.2

50. For a one-tailed test (upper tail) at 93.7% confidence, Z = a. 1.50 b. 1.96 c. 1.645 d. 1.53

d. 1.53

Exhibit 9-9 The sales of a grocery store had an average of $8,000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8,250 per day. From past information, it is known that the standard deviation of the population is $1,200. 81. Refer to Exhibit 9-9. The value of the test statistic is a. 250 b. 8000 c. 8250 d. 1.67

d. 1.67

45. For a one-tailed test (upper tail), a sample size of 18 at 95% confidence, t = a. 2.12 b. -2.12 c. -1.740 d. 1.740

d. 1.740

31. In the past, 75% of the tourists who visited Chattanooga went to see Rock City. The management of Rock City recently undertook an extensive promotional campaign. They are interested in determining whether the promotional campaign actually increased the proportion of tourists visiting Rock City. The correct set of hypotheses is a. H0: P > 0.75 Ha: P <= 0.75 b. H0: P < 0.75 Ha: P >= 0.75 c. H0: P >= 0.75 Ha: P < 0.75 d. H0: P <= 0.75 Ha: P > 0.75

d. H0: P <= 0.75 Ha: P > 0.75

33. A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. Any over filling or under filling results in the shutdown and readjustment of the machine. To determine whether or not the machine is properly adjusted, the correct set of hypotheses is a. H0: μ < 12 Ha: μ <= 12 b. H0: μ <= 12 Ha: μ > 12 c. H0: μ ≠ 12 Ha: μ = 12 d. H0: μ = 12 Ha: μ ≠ 12

d. H0: μ = 12 Ha: μ ≠ 12

26. If a hypothesis test leads to the rejection of the null hypothesis, a. a Type II error must have been committed b. a Type II error may have been committed c. a Type I error must have been committed d. a Type I error may have been committed

d. a Type I error may have been committed

13. The power curve provides the probability of a. correctly accepting the null hypothesis b. incorrectly accepting the null hypothesis c. correctly rejecting the alternative hypothesis d. correctly rejecting the null hypothesis

d. correctly rejecting the null hypothesis

9. The p-value a. is the same as the Z statistic b. measures the number of standard deviations from the mean c. is a distance d. is a probability

d. is a probability

53. For a one-tailed hypothesis test (upper tail) the p-value is computed to be 0.034. If the test is being conducted at 95% confidence, the null hypothesis a. could be rejected or not rejected depending on the sample size b. could be rejected or not rejected depending on the value of the mean of the sample c. is not rejected d. is rejected

d. is rejected

36. If a hypothesis is rejected at the 5% level of significance, it a. will always be rejected at the 1% level b. will always be accepted at the 1% level c. will never be tested at the 1% level d. may be rejected or not rejected at the 1% level

d. may be rejected or not rejected at the 1% level

1.The sum of the values of Alpha and Beta a. always add up to 1.0 b. always add up to 0.5 c. is the probability of Type II error d. none of these alternatives is correct

d. none of these alternatives is correct

Exhibit 9-6 A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. 73. Refer to Exhibit 9-6. At 95% confidence, it can be concluded that the mean age is a. not significantly different from 24 b. significantly different from 24 c. significantly less than 24 d. significantly more than 24

d. significantly more than 24

4. The probability of committing a Type I error when the null hypothesis is true is a. the confidence level b. Beta c. greater than 1 d. the Level of Significance

d. the Level of Significance

18. In hypothesis testing if the null hypothesis has been rejected when the alternative hypothesis has been true, a. a Type I error has been committed b. a Type II error has been committed c. either a Type I or Type II error has been committed d. the correct decision has been made

d. the correct decision has been made