Chapter 08 - Quiz

Chapter 8Hypothesis Testing

True/False

1. The further the hypothesized mean is from the actual mean the greater the power of the test. Answer: True Difficulty: Medium (REF)

2. The manager of the quality department for a tire manufacturing company wants to know the average tensile strength of rubber used in making a certain brand of radial tire. She knows the population standard deviation and uses a Z test to test the null hypothesis that the mean tensile strength is 800 pounds per square inch. The calculated Z test statistic is a positive value that leads to a p-value of .067 for the test. If the significance level is .10, the null hypothesis would be rejected. Assume that the population of pressure values is normally distributed. Answer: False Difficulty: Medium

Use the following information to answer questions 3-4:The manager of the quality department for a tire manufacturing company wants to know the average tensile strength of rubber used in making a certain brand of radial tire. The population is normally distributed and the population standard deviation is known. She uses a Z test to test the null hypothesis that the mean tensile strength is less than or equal to 800 pounds per square inch. The calculated Z test statistic is a positive value that leads to a p-value of .067 for the test.

3. If the significance level is .10, the null hypothesis would be rejected. Answer: True Difficulty: Medium

4. If the significance level is .05, the null hypothesis would be rejected. Answer: False Difficulty: Medium

Use the following information to answer questions 5-6:The manager of the quality department for a tire manufacturing company wants to know the average tensile strength of rubber used in making a certain brand of radial tire. The population is normally distributed and the population standard deviation is known. She uses a Z test to test the null hypothesis that the mean tensile strength is 800 pounds per square inch. The calculated Z test statistic is a positive value that leads to a p-value of .045 for the test.

5. If the significance level () is .01, the null hypothesis would be rejected. Answer: False Difficulty: Medium

Bowerman, Essentials of Business Statistics, 2/e 226

6. If the significance level () is .05, the null hypothesis would be rejected. Answer: True Difficulty: Medium

7. A Type I error is rejecting a true null hypothesis. Answer: True Difficulty: Medium

8. The larger the p-value, the more we doubt the null hypothesis. Answer: False Difficulty: Medium

9. A Type II error is failing to reject a false null hypothesis. Answer: True Difficulty: Medium (REF)

10. You cannot make a Type II error when the null hypothesis is true. Answer: True Difficulty: Medium (REF)

11. For a hypothesis test about a population proportion or mean, if the level of significance is less than the p-value, the null hypothesis is rejected. Answer: False Difficulty: Medium

12. Alpha () is the probability that the test statistic would assume a value as or more extreme than the observed value of the test. Answer: False Difficulty: Medium

13. Everything else being constant, increasing the sample size decreases the probability of committing a Type II error. Answer: True Difficulty: Medium

14. The null hypothesis is a statement that will be accepted only if there is convincing sample evidence that it is true. Answer: False Difficulty: Easy

15. The power of a statistical test is the probability of rejecting the null hypothesis when it is true. Answer: False Difficulty: Medium

Bowerman, Essentials of Business Statistics, 2/e227

16. As the level of significance increases, we are more likely to reject the null hypothesis. Answer: True Difficulty: Medium

17. A test statistic is computed from sample data in hypothesis testing and is used in making a decision about whether or not to reject the null hypothesis. Answer: True Difficulty: Medium

18. When conducting a hypothesis test about a single mean, other relevant factors held constant, increasing the level of significance from .05 to .10 will reduce the probability of a Type I error. Answer: False Difficulty: Medium

19. When conducting a hypothesis test about a single mean, other relevant factors held constant, increasing the level of significance from .05 to .10 will reduce the probability of a Type II error. Answer: True Difficulty: Medium (REF)

20. The null hypothesis always includes an equal (=) sign. Answer: True Difficulty: Easy

21. The level of significance indicates the probability of rejecting a false null hypothesis. Answer: False Difficulty: Medium (REF)

22. When conducting a hypothesis test about a single mean, reducing the level of significance () will increase the size of the rejection region. Answer: False Difficulty: Medium

23. When the null hypothesis is not rejected, there is no possibility of making a Type I error. Answer: True Difficulty: Medium

24. When the null hypothesis is true, there is no possibility of making a Type I error. Answer: False Difficulty: Medium


Multiple Choice

25. When testing the null hypothesis about a single population variance, one compares the computed test statistic for significance with a value from the ___________ distribution. A) t B) Z C) Binomial D) Chi-square Answer: D Difficulty: Medium

26. When testing a null hypothesis about a single population mean and the population standard deviation is unknown, if the sample size is less than 30, one compares the computed test statistic for significance with a value from the ___________ distribution. A) t B) Z C) Binomial D) Chi-square Answer: A Difficulty: Medium

27. Which statement is incorrect? A) The null hypothesis contains the equality sign. B) When a false null hypothesis is not rejected, a Type II error has occurred. C) If the null hypothesis is rejected, it is concluded that the alternative hypothesis is true. D) If we fail to reject the null hypothesis, then it is proven that null hypothesis is true. Answer: D Difficulty: Medium (REF)

28. For a given hypothesis test, if we do not reject H0, and H0 is true. A) No error has been committed. B) Type I error has been committed. C) Type II error has been committed. D) Type III error has been committed. Answer: A Difficulty: Easy

29. If a null hypothesis is rejected at a significance level of .01, it will ______ be rejected at a significance level of .05 A) Always B) Sometimes C) Never Answer: A Difficulty: Hard


30. If a null hypothesis is rejected at a significance level of .05, it will ______ be rejected at a significance level of .01 A) Always B) Sometimes C) Never Answer: B Difficulty: Hard

31. If a null hypothesis is not rejected at a significance level of .05, it will ______ be rejected at a significance level of .01 A) Always B) Sometimes C) Never Answer: C Difficulty: Hard

32. When testing a hypothesis about a single proportion, if np > 5 and n(1 – p) > 5, then Z statistic is ___________ used. A) Always B) Sometimes C) Never Answer: A Difficulty: Medium

33. If a two-sided null hypothesis is rejected for a single mean at a given significance level, the corresponding one- sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will_________ be rejected at the same significance level. A) Always B) Sometimes C) Never Answer: A Difficulty: Hard

34. If a two-sided null hypothesis can not be rejected for a single mean at a given significance level, then the corresponding one-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will_________ be rejected at the same significance level. A) Always B) Sometimes C) Never Answer: B Difficulty: Hard


35. If a one-sided null hypothesis for a single mean can not be rejected at a given significance level, then the corresponding two-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will_________ be rejected at the same significance level. A) Always B) Sometimes C) Never Answer: C Difficulty: Hard

36. If a one-sided null hypothesis is rejected at a given significance level, then the corresponding two-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will_________ be rejected at the same significance level. A) Always B) Sometimes C) Never Answer: B Difficulty: Hard

37. Type II error is defined as the probability of ________________ H0, when it should ___________. A) failing to reject; be rejected B) failing to reject; not be rejected C) rejecting, not be rejected D) rejecting, rejected Answer: A Difficulty: Medium

38. A professional basketball player is averaging 21 points per game. He will be retiring at the end of this season. The team has multiple options to replace him. However, the owner feels that signing a replacement is only justified, if he can average more than 22 points per game. Which of the following are the appropriate hypotheses for this problem? A) H0: ≤ 21 vs. H: > 21 B) H0: ≤ 22 vs. H: > 22 C) H0: 21 vs. H: < 21 D) H0: 22 vs. H: < 22 Answer: B Difficulty: Hard

39. A decision in a hypothesis test can be made by using a A) p-value B) Rejection point C) A and B D) None of the above Answer: C Difficulty: Medium


40. A _____ is the likelihood of a sample result assuming that the null hypothesis is true. A) Type II error B) Type I error C) Rejection point D) p-value Answer: D Difficulty: Medium

41. What value(s) of alpha would we reject H0 for greater than 10 if = 11, s = 2, and n = 36? A) .05 and .01 B) .01 and .001 C) .001 D) All of the above Answer: A Difficulty: Medium

42. When carrying out a large sample test of H0: = 10 vs. Ha: > 10 by using a rejection point, we reject H0 at level of significance when the calculated test statistic is: A) Less than zB) Less than -zC) Greater than z/2

D) Greater than zE) Less than the p value Answer: D Difficulty: Medium

43. When carrying out a large sample test about a population proportion p where we are testing H0: p = .4 versus Ha: p < .4 and z is the calculated test statistic, we reject H0 at level of significance when: A) z < -z/2

B) z < -zC) z > zD) p-value < E) Both B and D Answer: E Difficulty: Medium


44. When carrying out a large sample test of H0: = 10 vs. Ha: 10 by using a p-value, we reject H0 at level of significance when the p-value is: A) Greater than /2 B) Greater than C) Less than D) Less than /2 E) Less than ZAnswer: C Difficulty: Medium

45. If a null hypothesis is not rejected at a significance level of .01, it will_________ rejected at a significance level of .05 A) Always B) Sometimes C) Never Answer: B Difficulty: Medium

46. In a two-sided hypothesis test if the p value is less than : A) H0 is rejected. B) H0 is not rejected. C) H0 may or may not be rejected depending on the sample size n. D) Additional information is needed and no conclusion can be reached about whether H0 should be rejected. Answer: A Difficulty: Easy

47. When conducting a hypothesis test about a single mean, at a given level of significance, as the sample size n increases, the power of the test: A) Will decrease. B) Will increase. C) May increase or decrease D) Remains the same Answer: B Difficulty: Medium

48. When conducting a hypothesis test about a single mean, at a given level of significance, as the sample size n increases, the probability of a Type II error: A) Will decrease. B) Will increase. C) May increase or decrease D) Remains the same Answer: A Difficulty: Medium


49. For the following hypothesis test where H0: ≤ 10 vs. Ha: > 10, we reject H0 at level of significance and conclude that the true mean is greater than 10 when the true mean is really 8. Based on this information we can state that we have: A) Made a Type I error B) Made a Type II error C) Made a correct decision D) Increased the power of the test Answer: A Difficulty: Medium

50. For the following hypothesis test where H0: ≤ 10 vs. Ha: > 10, we reject H0 at level of significance and conclude that the true mean is greater than 10 when the true mean is really 14. Based on this information we can state that we have: A) Made a Type I error B) Made a Type II error C) Made a correct decision D) Increased the power of the test Answer: C Difficulty: Medium

51. The power of a statistical test is the probability of ______________ the null hypothesis when it is ________. A) Not rejecting, false B) Not rejecting, true C) Rejecting, false D) Rejecting, true Answer: C Difficulty: Medium

52. Which of the following signs would not be used in stating a null hypothesis? A) ≤ B) = C) D) < E) B and D Answer: D Difficulty: Medium

53. When conducting a hypothesis test about a single mean, at a given level of significance, holding all other relevant factors constant, using a sample of n = 29 will result in a _________ rejection region than using a sample of n = 10 A) Wider B) Narrower C) Neither A or B, they will be the same Answer: B Difficulty: Hard


54. The average customer waiting time at a fast food restaurant has been 7.5 minutes. The customer waiting time has a normal distribution. The manager claims that the use of a new system will decrease average customer waiting time in the store. What is the null and alternative hypothesis for this scenario? A) H0: = 7.5 and HA 7.5 B) H0: ≤ 7.5 and HA > 7.5 C) H0: 7.5 and HA < 7.5 D) H0: > 7.5 and HA 7.5 E) H0: > 7.5 and HA ≤ 7.5 Answer: C Difficulty: Medium

Use the following information to answer questions 55-58:The average waiting time per customer at a fast food restaurant has been 7.5 minutes. The customer waiting time has a normal distribution. The manager claims that the use of a new cashier system will decrease the average customer waiting time in the store.

55. A random sample of 12 customer transactions has been recorded. At a significance level of .05, what is the rejection point condition? We would reject the null hypothesis if: A) Z < -1.645 B) Z > 1.645 C) t > 1.796 D) t < -1.796 E) t < -1.782 Answer: D Difficulty: Medium

56. A random sample of 250 customer transactions has been recorded. At a significance level of .05, what is the rejection point condition? We would reject the null hypothesis if: A) Z < -1.645 B) Z > 1.645 C) Z > 1.96 D) Z < -1.96 E) Z < -2.33 Answer: A Difficulty: Easy


57. Based on a random sample of 16 customer transactions the mean waiting time is 6.3 minutes and the standard deviation is 2 minutes per customer. What is the value of the test statistic? A) t = -1.2 B) t = 2.4 C) t = -2.4 D) t = -0.6 E) t = 9.6 Answer: C Difficulty: Medium

58. Based on a random sample of 16 customer transactions the mean waiting time is 6.3 minutes and the standard deviation is 2 minutes per customer. What is the p-value? A) .1151 B) .0082 C) .2302 D) .0164 E) .0000 Answer: B Difficulty: Medium

Use the following information to answer questions 59-60:A major airline company is concerned that its proportion of late arrivals has substantially increased in the past month. Historical data shows that on the average 18% of the company airplanes have arrived late. In a random sample of 1,240 airplanes, 310 airplanes have arrived late. If we are conducting a hypothesis test of a single proportion to determine if the proportion of late arrivals has increased:

59. What is the correct statement of null and alternative hypothesis? A) H0: p < .18 and HA: p .18 B) H0: p ≤ .18 and HA: p > .18 C) H0: p = .18 and HA: p .18 D) H0: p > .18 and HA: p ≤ .18 E) H0: p ≤ .20 and HA: p > .20 Answer: B Difficulty: Hard

60. What is the value of the calculated test statistic? A) Z = 6.416 B) Z = 3.208 C) Z = -3.208 D) Z = -6.416 E) Z = 1.833 Answer: A Difficulty: Hard



Fill-in-the-Blank

61. The rejection of a true null hypothesis is called a ______________ error. Answer: Type I Difficulty: Medium

62. When testing a hypothesis about a single mean, if the sample size is 51, and the population standard deviation is known, the correct test statistic to use is ___________. Answer: Z Difficulty: Medium

63. When testing a hypothesis about a single mean, if the sample size is 20, and the population standard deviation is unknown, the correct test statistic to use is ___________. Answer: t Difficulty: Medium

64. When testing a hypothesis about a single mean, sample size of 200 is selected from a normally distributed population. If the population standard deviation is known, the correct test statistic to use is ___________. Answer: Z Difficulty: Hard

65. The _____ of a statistical test is the probability of rejecting the null hypothesis when it is false. Answer: Power Difficulty: Medium

66. __________is the probability of not rejecting H0 when H0 is false. Answer: Type II error or Difficulty: Medium

67. For a fixed sample size, the lower we set , the higher is the ___________. Answer: Type II error or Difficulty: Medium

68. Assuming a fixed sample size, as (Type I error) decreases, (Type II error) ___________. Answer: increases Difficulty: Medium

69. As the type II error of statistical test increases, the power of the test _____________. Answer: decreases Difficulty: Medium


70. A null hypothesis is not rejected at given level of significance. As the assumed value of the mean gets further away from the true population mean, the type II error will _____________. Answer: decrease Difficulty: Medium

71. Increasing the sample size __________ the probability of committing a type II error. Answer: decreases Difficulty: Medium

72. The _____ hypothesis is not rejected unless there is sufficient sample evidence to do so. Answer: Null Difficulty: Medium

73. The _____ hypothesis will be accepted only if there is convincing sample evidence that it is true. Answer: Alternative Difficulty: Medium

74. Assuming that the null hypothesis is true, the ______________ is the probability of observing a value of the test statistic that is at least as extreme as the value actually computed from the sample data. Answer: p-value Difficulty: Medium

75. The value of the test statistic is compared with a(n) _______________ in order to decide whether the null hypothesis can be rejected. Answer: rejection point Difficulty: Medium

76. A(n) _________ hypothesis is the statement that is being tested. It usually represents the status quo and it is not rejected unless if there is convincing sample evidence that it is false. Answer: null Difficulty: Easy


Essay

77. Test H0: ≤ 8 versus HA: > 8, given = .01, n = 25, = 8.112, and s = .16. Assume the sample is selected from a normally distributed population. Answer: Reject H0

0

.01,24

0

: 8 : 8

8.112 83.5

.16

252.492

3.5 2.492,

AH H

t

t

reject H

Difficulty: Medium

78. Test H0: 22 versus HA: < 22, given = .01, n = 100, = 21.431, and s = 1.295. Answer: Reject H0

0

.01

0

: 22 : 22

21.431 22 .5694.394

1.295 .1295100

2.33

4.394 2.33,

AH H

Z

Z

reject H

Difficulty: Medium

79. Assuming a normal population, use the data: 15, 19, 12, 14, 23, and 13 to test H0: = 18 versus HA: 18 at =.05. Answer: Fail to reject H0

0

.025,5

0

: 18 : 18

16, 4.195

16 181.167

4.195

62.571

1.167 2.571, failed to reject H

AH H

X s

t

t

Difficulty: Hard


80. Given sample data: .612, .619, .628, .631, .640, .643, .649, .655, .663, and .679, test H0: ≤ .625 versus HA: > .625 at =.10. Answer: Reject H0

H0:.625 HA: >.625 = .6419, s = .02049

t10,9 = 1.3832.61 > 1,383, Reject H0

Difficulty: Hard

81. Determine the p-value for H0: p ≤ .5 versus HA: p > .5 when n = 225 and = .54. Answer: .1151

.54 .51.2

(.5)(.5)225

.5 .3849 .1151

Z

p value

Difficulty: Medium

82. Determine the p-value for H0: p = .5 versus HA: p .5 when n = 225 and = .54. Answer: .2302

.54 .51.2

(.5)(.5)225

2(.5 .3849) .2302

Z

p value

Difficulty: Medium

83. Determine the p-value for H0: 95 versus HA: < 95 when X = 90.2, s = 9.92, and n = 37. Answer: .0016

90.2 95 4.82.94

9.92 1.630837

.5 .4984 .0016

Z

p value

Difficulty: Medium

84. Determine the p-value for H0: = 95 versus HA: 95 when = 90.2, s = 9.92, and n =


37. Answer: .0032

90.2 95 4.82.94

9.92 1.630837

2(.5 .4984) .0032

Z

p value

Difficulty: Medium

85. Test H0: = 32 versus HA: > 32 when = 36, s = 1.6, and n = 30 at = .05. Answer: Reject H0

0

.05,29

0

: 32 : 32

36 3213.693

1.6

301.699

13.693 1.699, .

AH H

t

t

reject H

Difficulty: Medium

86. In testing H0: = 23 versus HA: > 23 when =26, s = 6, and n = 20, what is the value of the t-statistic? Answer: 2.24

26 232.24

6

20

t

Difficulty: Easy

87. In testing H0: ≤ 23 versus HA: > 23 when = 26, s = 6, and n = 30, what is the value of the z-statistic? Answer: 2.74

26 232.74

6

30

Z

Difficulty: Easy


88. In testing H0: p = .2 versus HA: p .2 with = .26 and n = 100, what is the value of the z-statistic? Answer: 1.5

.26 .21.5

(.2)(.8)100

Z

Difficulty: Easy

89. Test H0: p = .2 versus HA: p .2 with = .26 and n = 100 at alpha = .05. Answer: Fail to reject H0

0

.025

0

: .2 : .2

.26 .21.5

(.2)(.8)

1001.96

1.5 1.96,

AH p H p

Z

Z

failed to reject H

Difficulty: Medium

90. In testing H0: p .33 versus HA: p < .33 with = .20 and n = 100, what is the value of the z-statistic? Answer: -2.77

.2 .332.77

(.33)(.67)100

Z

Difficulty: Medium

91. Test at = .05 H0: p = .33 versus HA: p < .33 with = .20 and n = 100. Answer: Reject H0

0

.05

0

: .33 : .33

.2 .332.77

(.33)(.67)

1001.645

2.77 1.645,

AH p H p

Z

Z

reject H

Difficulty: Medium


92. Test H0: ≤ .95 versus HA: > .95 when = .99, s = .12, and n = 24 at alpha = .05. Assume a normally distributed population. Answer: Reject H0

0

.05,23

0

: .95 : .95

.99 .951.633

.12

241.714

1.633 1.714, failed to reject .

AH H

t

t

H

Difficulty: Medium

93. Test H0: p .7 versus HA: p < .7 with = .63 and n = 100 at = .01. Answer: Fail to reject H0

0

.01

0

: .7 : .7

.63 .71.53

(.7)(.3)

1002.33

1.53 2.33, we failed to reject H

AH p H p

Z

Z

Difficulty: Medium

94. Test H0: ≤ 3.0 versus HA: > 3.0 when = 3.44, s = .57, and n = 13 at a significance level of .05. Assume population normality. Answer: Reject H0

0

.05,12

0

: 3 : 3

3.44 3.02.783

.57

131.782

2.783 1.782, reject .

AH H

t

t

H

Difficulty: Medium


95. Test H0: 2.5 versus HA: < 2.5 when = 2.46, s = .05, and n = 26 at = .10. Assume that the population from which the sample is selected is normally distributed. Answer: Reject H0

0

.10,25

0

: 2.5 : 2.5

2.46 2.54.08

.05

261.318

4.08 1.318, reject .

AH H

t

t

H

Difficulty: Medium

96. Can it be established at = .05 that a majority of students favor the plus/minus grading system at a university if in a random sample of 500 students, 270 favor the system? Answer: Yes.

0

.05

0

: .5 : .5

270ˆ .54

500.54 .50

1.789(.5)(.5)

5001.645

1.789 1.645, we reject H

AH p H p

p

Z

Z

Difficulty: Medium

97. Is there enough evidence to establish that the mean population age exceeds 42? Write HA for this question. Answer: > 42 Difficulty: Easy


98. Does the sample evidence indicate that the average time an employee stays with a company in their current positions is less than 3 years? A random sample of 50 employees yielded a mean of 2.79 years and s = .76. Use = .01. Answer: No, there is not sufficient evidence.

0

.01

0

: 3 : 3

2.79 31.954

.76

502.33

1.954 2.33, we failed to reject .

AH H

Z

Z

H

Difficulty: Medium

Use the following information to answer questions 99-106A random sample of 100 European professional soccer players has an average age of 27 years. The sample standard deviation is 4 years. We would like to decide if there is enough evidence to establish that average age of European soccer players is more than 26 years.

99. Write the null hypothesis. Answer: H0: ≤ 26 Difficulty: Easy (AS)

100. Write the alternative hypothesis. Answer: HA: > 26 Difficulty: Easy (AS)

101. What is the rejection point (given in terms of the value of the test statistic) at = .05? Answer: z = 1.645 Difficulty: Medium (AS)

102. What is the rejection point (given in terms of the value of the test statistic) at = .01? Answer: z = 2.33 Difficulty: Easy (AS)

103. What is the sample value of the test statistic? Answer: z = 2.5

27 262.5

4

100

Z

Difficulty: Medium (AS)


104. What is the decision at = .05? Answer: Reject H0

27 262.5

4

100

Z

2.5 > 1.645, therefore, reject H0. Difficulty: Medium (AS)


27 262.5

4

100

Z

2.5 > 2.33, therefore, reject H0. Difficulty: Medium (AS)

106. What is the p-value for this test? Answer: .0062

27 262.5

4

100.5 .4938 .0062

Z

p value

Difficulty: Medium (AS)

Use the following information to answer questions 107-114:Based on a random sample of 25 units of product X, the average weight is 102 lbs., and the sample standard deviation is 10 lbs. We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lbs. Assume the population is normally distributed.

107. Write the null hypothesis. Answer: H0: = 100 Difficulty: Easy

108. Write the alternative hypothesis. Answer: HA: > 100 Difficulty: Easy


109. What is the rejection point (given in terms of the value of the test statistic) at = .05? Answer: t = 1.711t24, 05 = 1.711 Difficulty: Medium

110. What is the rejection point (given in terms of the value of the test statistic) at = .01? Answer: t = 2.492t24, 01 = 2.492 Difficulty: Medium

111. What is the sample value of the test statistic? Answer: t = 1.0

102 1001

10

25

Z

Difficulty: Medium

112. What is the decision at = .05? Answer: Fail to reject H0

1 < 1.711 Difficulty: Medium

113. What is the decision at = .01? Answer: Fail to reject H0

1 < 2.492 Difficulty: Medium

114. What is the p-value for this test? Answer: Greater than .10 Difficulty: Medium

Use the following information to answer questions 115-122:A recent study conducted by the state government attempts to determine whether the voting public supports further increase in cigarette taxes. The opinion poll recently sampled 1500 voting age citizens. 1020 of the sampled citizens were in favor of an increase in cigarette taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66.

115. Write the null hypothesis for this problem. Answer: H0: p ≤ .66 Difficulty: Easy


116. Write the alternative hypothesis. Answer: HA: p > .66 Difficulty: Easy

117. What is the rejection point (given in terms of the value of the test statistic) at = .10? Answer: Z = 1.28 Difficulty: Medium

118. What is the rejection point (given in terms of the value of the test statistic) at = .01? Answer: Z = 2.33 Difficulty: Medium

119. What is the sample value of the test statistic? Answer: Z = 1.635

1020ˆ .68

1500.68 .66

1.635(.66)(.34)

1500

p

Z

Difficulty: Medium


1.635 > 1.28 Difficulty: Medium

121. What is the decision at = .05 Answer: Fail to reject H0

1.635 < 1.645 Difficulty: Medium

122. What is the p-value for this test? Answer: .051.5 - .449 = .051 Difficulty: Medium


123. A microwave manufacturing company has just switched to a new automated production system. Unfortunately, the new machinery has been frequently failing and requiring repairs and service. The company has been able to provide its customers with a completion time of 6 days or less. To analyze whether the completion time has increased, the production manager took a sample of 36 jobs and found that the sample mean completion time was 6.5 days with a sample standard deviation of 1.5 days. At a significance level of .10, test whether the completion time has increased. Answer: Completion time has increased.

0

.10,35 0

: 6 : 6

6.5 62

1.5

361.30 1.31

AH H

t

t or reject H

Difficulty: Medium

124. The accompanying data are the times in seconds that it took a sample of employees to assemble a component at Ental Industries manufacturing facility. Assembly times are normally distributed. At the .05 significance level, can we conclude that the mean assembly time for this component is not equal to 3 minutes? Use HA: 180.

190 198 180 181 208 198199 176 174 183 188 165

Answer: Average assembly time is not equal to 3 minutes.

0

.05,11

0

: 180 : 180

186.67 12.471

1.796

186.67 1801.852

12.471

121.852 1.796,

A

calc

H H

X s

t

t

reject H

Difficulty: Medium


125. A null hypothesis H0: 2.4 is not rejected at a significance level of 0.04. ( = 0.04). The standard deviation for the normally distributed population is known to be 0.40. Determine the Type II error, if we assume that the actual mean is 2.125 based on a sample size of 16. Answer: .1587

.42.4 1.75 2.225

16

2.225 2.1251

.1(2.125 2.225) .3413

.5 .3413 .1587

Z

P

Difficulty: Hard

126. A null hypothesis H0: 2.4 accepted at a significance level of 0.04. ( = 0.04). The standard deviation for the normally distributed population is known to be 0.40. Assume that the actual mean is 2.125 based on a sample size of 16, and determine the power of the test. Answer:

.42.4 1.75 2.225

16

2.225 2.1251

.1(2.125 2.225) .3413

.5 .3413 .1587

1 1 .1587 .8413

Z

P

Power

Difficulty: Hard

Use the following information to answer questions 127-128:A null hypothesis H0: 2.4 is not rejected at a significance level of 0.04. ( = 0.04). The population appears to be normally distributed. The standard deviation for the population is known to be 0.40.


127. Assume that the actual mean is 2.175 based on a sample size of 16, and determine the probability of a Type II error. Answer: .3085

.42.4 1.75 2.225

16

2.225 2.175.50

.1(2.125 2.175) .1915

.5 .1915 .3085

Z

P

Difficulty: Hard

128. Assume that the actual mean is 2.175 based on a sample size of 16, and determine the power of the test. Answer: .6915

.42.4 1.75 2.225

16

2.225 2.175.50

.1(2.125 2.175) .1915

.5 .1915 .3085

1 .3085 .6915

Z

P

Power

Difficulty: Hard

Use the following information to answer questions 129-131:A null hypothesis H0: 2.4 is not rejected at a significance level of 0.05 ( = 0.05). The standard deviation for the normally distributed population is known to be 0.36.

129. Assume that the actual mean is 2.125 based on a sample size of 36, and determine the probability of a Type II error. Answer: 0.0016

.362.4 1.645 2.3013

36

2.3013 2.1752.9353

.06(2.125 2.3013) .4984

.5 .4984 .0016

Z

P

Difficulty: Hard



130. Assume that the actual mean is 2.125 based on a sample size of 36 and determine the power of the test. Answer: .9984

.362.4 1.645 2.3013

36

2.3013 2.1752.9353

.06(2.125 2.3013) .4984

.5 .4984 .0016

1 .0016 .9984

Z

P

Power

Difficulty: Hard

131. In addition the firm desires to guard against Type II error (not rejecting the null hypothesis

erroneously), when the true mean is less than 2.2 at a level of .02 ( ) . How large a sample should be taken? Answer: 45

2

2

(1.645 2.05)(.36)44.23 45

(2.4 2.2)n

Difficulty: Hard

132. A null hypothesis H0: = 2.4 is tested at a significance level of 0.05 ( = 0.05). The standard deviation for the normally distributed population is known to be 0.40. In addition, the firm desires to guard against Type II error (not rejecting the null hypothesis erroneously), when the true mean is less than 2.25 at a level of .01 (). How large a sample should be taken? Answer: 131

2

2

(1.96 2.33)(.40)130.874 131

(2.4 2.25)n

Difficulty: Hard

Multiple Choice

Use the following information to answer questions 133-136:A mail-order business prides itself in its ability to fill customers’ orders in less than six calendar days, on average. Periodically, the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders. On one occasion when a sample of 39 orders was selected, the average number of days was 6.65 with a sample standard deviation of 1.5 days.


133. Set up the null and alternative hypotheses to test whether the standard is being metA) HO: μ = 6 vs. HA: μ ≠ 6B) HO: μ ≥ 6.65 vs. HA: μ < 6.65C) HO: μ ≥ 6 vs. HA: μ < 6D) HO: μ ≠ 6 vs. HA: μ = 6E) HO: μ ≤ 6 vs. HA: μ > 6Answer: C Difficulty: Medium

134. Calculate the appropriate test statistic to test the hypotheses.A) 2.71B) 16.90C) 0.65D) -2.71E) 3.31Answer: A Difficulty: Medium

135. What is the rejection point for α = .10 to test the hypotheses.A) -1.28B) -1.96C) -2.33D) 1.28E) 1.96Answer: C Difficulty: Easy

136. How much evidence do we have that the standard is being met?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: A Difficulty: Easy

Use the following information to answer questions 137-140:A random sample of 80 companies who announced corrections to their balance sheets took a mean time of 8.1 days for the time between balance sheet construction and the complete audit. The standard deviation of these times was 1.3 days.


137. Set up the null and alternative hypotheses to provide evidence supporting the claim that μ is greater than 7.5 days which was the previous year amount.A) HO: μ = 7.5 vs. HA: μ ≠ 7.5B) HO: μ ≥ 7.5 vs. HA: μ < 7.5C) HO: μ ≥ 8.1 vs. HA: μ < 8.1D) HO: μ ≠ 7.5 vs. HA: μ = 7.5E) HO: μ ≤ 7.5 vs. HA: μ > 7.5Answer: E Difficulty: Medium (AS)

138. Calculate the appropriate test statistic to test the hypotheses.A) -4.13B) 36.92C) 4.71D) -4.71E) 4.13Answer: E Difficulty: Medium (AS)

139. What is the rejection point for α = .001 to test the hypotheses.A) 2.575B) 3.09C) -1.96D) -2.575E) -3.09Answer: B Difficulty: Easy (AS)

140. How much evidence do we have that the time is longer than 7.5 days?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: E Difficulty: Easy (AS)

Use the following information to answer questions 141-144:The manufacturer of an over-the-counter heartburn relief mediation claims that it product brings relief in less than 3.5 minutes, on average. To be able to make this claim the manufacturer was required by the FDA to present statistical evidence in support of the claim. The manufacturer reported that for a sample of 50 heartburn sufferers, the mean time to relief was 3.3 minutes and the standard deviation was 1.1 minutes.


141. Set up the null and alternative hypotheses to test the manufacturer’s claimA) HO: μ = 3.3 vs. HA: μ ≠ 3.3B) HO: μ ≥ 3.5 vs. HA: μ < 3.5C) HO: μ ≥ 3.3 vs. HA: μ < 3.3D) HO: μ ≠ 3.5 vs. HA: μ = 3.5E) HO: μ ≤ 3.5 vs. HA: μ > 3.5Answer: B Difficulty: Medium

142. Calculate the appropriate test statistic to test the hypotheses.A) 1.29B) 9.09C) -1.29D) -2.58E) -9.09Answer: C Difficulty: Medium

143. Calculate the p-value that corresponds to the test statistic.A) 0.0985B) 0.0001C) 0.4015D) 0.005E) -0.985Answer: A Difficulty: Medium

144. How much evidence do we have that the claim is true?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: B Difficulty: Easy

Use the following information to answer questions 145-148:A company has developed a new ink-jet cartridge for its printer that it believes has a longer life-time on average than the one currently being produced. To investigate its length of life, 225 of the new cartridges were tested by counting the number of high-quality printed pages each was able to produce. The sample mean and standard deviation were determined to be 1511.4 pages and 35.7 pages, respectively. The historical average lifetime for cartridges produced by the current process is 1502.5 pages.


145. Set up the null and alternative hypotheses to test whether the mean lifetime of the new cartridges exceeds that of the old cartridges.A) HO: μ = 1502.5 vs. HA: μ ≠ 1502.5B) HO: μ ≥ 1511.4 vs. HA: μ < 1511.4C) HO: μ ≥ 1502.5 vs. HA: μ < 1502.5D) HO: μ ≠ 1502.5 vs. HA: μ = 1502.5E) HO: μ ≤ 1502.5 vs. HA: μ > 1502.5Answer: E Difficulty: Medium

146. Calculate the appropriate test statistic to test the hypotheses.A) 56.09B) 3.74C) 22.34D) -3.74E) -22.34Answer: B Difficulty: Medium

147. What is the rejection point for α = .05 to test the hypotheses.A) 1.645B) -1.645C) 1.96D) 1.28E) -1.96Answer: A Difficulty: EasyRefer To: 08_13

148. How much evidence do we have that the new cartridge is better than the old?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: E Difficulty: EasyRefer To: 08_13

Use the following information to answer questions 149-152:A study investigated the relationship of employment status to mental health. A sample of 49 unemployed men took a mental health examination measuring present mental health with lower values indicating better mental health. Their mean score was 10.94 and a standard deviation of 4.90.


149. Set up the null and alternative hypotheses if we wish to test the research hypothesis that the mean score for all unemployed men exceeds 10.A) HO: μ = 10 vs. HA: μ ≠ 10B) HO: μ ≥ 10.94 vs. HA: μ < 10.94C) HO: μ ≥ 10 vs. HA: μ < 10D) HO: μ ≠10 vs. HA: μ = 10E) HO: μ ≤ 10 vs. HA: μ > 10Answer: E Difficulty: Medium

150. Calculate the appropriate test statistic to test the hypotheses.A) 2.97B) -2.97C) 2.68D) 1.34E) -1.34Answer: D Difficulty: Medium

151. Calculate the p-value for the test statistic.A) 0.0901B) 0.0037C) 0.0015D) -0.0015E) -0.0901Answer: A Difficulty: Medium

152. How much evidence do we have that the mean score exceeds 10?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: B Difficulty: Easy

Use the following information to answer questions 153-156:When 100 randomly selected car owners are surveyed, it is found that the mean length of time they plan to keep their car is 7.01 years, and the standard deviation is 3.74 years.


153. Set up the null and alternative hypotheses to test the claim that the mean for all car owners is less than 7.5 years.A) HO: μ = 7.5 vs. HA: μ ≠ 7.5B) HO: μ ≥ 7.5 vs. HA: μ < 7.5C) HO: μ ≥ 7.01 vs. HA: μ < 7.01D) HO: μ ≠ 7.5 vs. HA: μ = 7.5E) HO: μ ≤ 7.5 vs. HA: μ > 7.5Answer: B Difficulty: Medium

154. Calculate the appropriate test statistic to test the hypotheses.A) -13.10B) -2.53C) -1.31D) 1.31E) 2.53Answer: C Difficulty: Medium

155. Calculate the p-value for the test statistic.A) -0.0951B) 0.0951C) 0.1902D) 0.0057E) –0.0057Answer: B Difficulty: Medium

156. How much evidence do we have that the mean years is less than 7.5?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: B Difficulty: Easy

Use the following information to answer questions 157-160:In a study of distances traveled by buses before the first major engine failure, a sample of 191 buses results in a mean of 96,700 miles and a standard deviation of 37,500 miles.


157. Set up the null and alternative hypotheses to test the claim that the mean distance traveled before a major engine failure is more than 90,000 miles.A) HO: μ = 90,000 vs. HA: μ ≠ 90,000B) HO: μ ≥ 90,000 vs. HA: μ < 90,000C) HO: μ ≥ 96,700 vs. HA: μ < 96,700D) HO: μ ≠ 90,000 vs. HA: μ = 90,000E) HO: μ ≤ 90,000 vs. HA: μ > 90,000Answer: E Difficulty: Medium (AS)

158. Calculate the appropriate test statistic to test the hypotheses.A) 2.47B) 34.13C) 478.16D) -34.13E) -2.47Answer: A Difficulty: Medium (AS)

159. Calculate the p-value corresponding to the test statistic.A) 0.0000B) 0.0068C) -0.0068D) 0.0136E) -0.0136Answer: B Difficulty: Medium (AS)

160. How much evidence do we have that the major engine failure will occur after 90,000 miles?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: D Difficulty: Easy (AS)

Use the following information to answer questions 161-164:A manufacturer of a chemical used in glue, attempting to control the amount of a hazardous chemical its workers are exposed to, has given instructions to halt production if the mean amount in the air exceeds 3.0ppm. A random sample of 50 air specimens produced the following statistics: sample mean = 3.1 ppm , sample standard deviation = 0.5 ppm.


161. Set up the null and alternative hypotheses that would be used to halt productionA) HO: μ = 3.0 vs. HA: μ ≠ 3.0B) HO: μ ≥ 3.0 vs. HA: μ < 3.0C) HO: μ ≥ 3.1 vs. HA: μ < 3.1D) HO: μ ≠ 3.0 vs. HA: μ = 3.0E) HO: μ ≤ 3.0 vs. HA: μ > 3.0Answer: E Difficulty: Medium

162. Calculate the appropriate test statistic to test the hypotheses.A) 1.00B) -1.00C) 2.80D) 1.41E) -1.41Answer: D Difficulty: Medium

163. Calculate the p-value for the test statistic.A) -0.0793B) 0.0398C) 0.1587D) -0.1587E) 0.0793Answer: E Difficulty: Medium

164. If the α level of shutting down production is set at 0.05, given this air sample should production be halted?A) YesB) NoAnswer: B Difficulty: Hard

Use the following information to answer questions 165-168:Standard x-ray machines should give radiation dosages below 5.00 mill roentgens. To test a certain x-ray machine a sample of 36 observations is taken with a mean of 4.13 m. and a standard deviation of 1.91 m.


165. Set up the null and alternative hypotheses to test whether this particular machine gives radiation below 5.00 mil (is in specification).A) HO: μ = 5 vs. HA: μ ≠ 5B) HO: μ ≥ 5 vs. HA: μ < 5C) HO: μ ≥ 4.13 vs. HA: μ < 4.13D) HO: μ ≠ 5 vs. HA: μ = 5E) HO: μ ≤ 5 vs. HA: μ > 5Answer: B Difficulty: Medium

166. Calculate the appropriate test statistic to test the hypotheses.A) -2.73B) -3.78C) -0.455D) 3.78E) 2.73Answer: A Difficulty: Medium

167. Calculate the p-value for this test statistic.A) 0.0032B) 0.0001C) 0.3264D) 0.0064E) -0.0032Answer: A Difficulty: Medium

168. How much evidence do we have that the machine is in specification?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: D Difficulty: Easy

Use the following information to answer questions 169-172:It is estimated that the average person in the US uses 123 gallons of water per day. Some environmentalists believe this figure is too high and conducted a survey of 40 randomly selected Americans. They find a mean of 113.03 gallons and a standard deviation of 25.99 gallons.


169. Set up the null and alternative hypotheses to test the claim that the water usage is less than the AWWA estimate.A) HO: μ = 123 vs. HA: μ ≠ 123B) HO: μ ≥ 123 vs. HA: μ < 123C) HO: μ ≥ 113.03 vs. HA: μ < 113.03D) HO: μ ≠ 123 vs. HA: μ = 123E) HO: μ ≤ 123 vs. HA: μ > 123Answer: B Difficulty: Medium

170. Calculate the appropriate test statistic to test the hypotheses.A) -0.38B) 2.43C) 0.38D) -15.34E) -2.43Answer: E Difficulty: Medium

171. Calculate the p-value for this test statistic.A) 0.4925B) -0.0075C) 0.0075D) 0.015E) 0.352Answer: C Difficulty: Medium

172. How much evidence do we have that the water usage is less than the AWWA estimate?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: D Difficulty: Easy

Use the following information to answer questions 173-177:A state education agency designs and administers high school proficiency exams. Historically, time to complete the exam was an average of 120 minutes. Recently the format of the exam changed and the claim has been made that the time to complete the exam has changed. A sample of 50 new exam times yielded an average time of 118 minutes. The standard deviation is assumed to be 5 minutes.


173. Set up the null and alternative hypothesis to test if the average time to complete the exam had changed from 120 minutes.A) H0 µ = 120 Ha µ ≠ 120B) H0 µ ≥ 120 Ha µ < 120C) H0 µ ≤ 120 Ha µ > 120D) H0 µ ≠ 120 Ha µ = 120E) H0 µ ≥ 118 Ha µ < 118Answer: A Difficulty: Medium

174. Calculate the test statistic to test these hypotheses.A) -2.82B) -6.32C) 5.64D) -5.64E) 2.82Answer: A Difficulty: Medium

175. Calculate the p-value.A) .0024B) -.0024C) .0000D) -.0048E) .0048Answer: E Difficulty: Medium

176. How much evidence do we have to reject the null hypothesis?A) No evidenceB) Some evidenceC) Strong evidenceD) Very Strong evidenceE) Extremely Strong evidenceAnswer: D Difficulty: Easy

177. Calculate a confidence interval to test the hypotheses at α = .01A) [116.18 119.82]B) [116.36 119.64]C) [116.61 119.39]D) [115.67 120.33]E) [115.82 120.18]Answer: A Difficulty: Medium


Use the following information to answer questions 178-182:A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses dressing is working properly when 8 ounces are dispensed. The standard deviation of the process is 0.15 ounces. A sample of 48 bottles is selected periodically, and the filling line is stopped if there is evidence that the mean amount dispensed is different from 8 ounces. Suppose that the mean amount dispensed in a particular sample of 48 bottles is 7.983 ounces.

178. Set up the null and alternative hypotheses to test the filling process.A) H0 µ ≠ 8 Ha µ = 8B) H0 µ ≤ 7.983 Ha µ > 7.983C) H0 µ ≤ 8 Ha µ > 8D) H0 µ ≥ 8 Ha µ < 8E) H0 µ = 8 Ha µ ≠ 8Answer: E Difficulty: Medium

179. Calculate the test statisticA) -0.785B) -1.57C) -3.04D) 1.57E) 0.785Answer: A Difficulty: Medium

180. Calculate the p-valueA) .216B) .432C) .0012D) .0582E) .1164Answer: B Difficulty: Medium

181. How much evidence do we have that the filling line should be stopped?A) No evidenceB) Some evidenceC) Strong evidenceD) Very Strong evidenceE) Extremely Strong evidenceAnswer: A Difficulty: Easy


182. Calculate a confidence interval to test the hypotheses at α = .05A) [7.947 8.019]B) [7.941 8.025]C) [7.933 8.033]D) [7.955 8.011]E) [7.916 8.050]Answer: B Difficulty: Medium

Use the following information to answer questions 183-187:The manager of a grocery store wants to determine whether the amount of water contained in 1 gallon bottle purchased from a nationally known manufacturer actually average 1 gallon. It is known from the manufacturer’s specifications that the standard deviation of the amount of water is equal to 0.02 gallon. A random sample of 32 bottles is selected, and the mean amount of water per 1 gallon can is found to be 0.995 gallon.

183. Set up the null and alternative hypotheses to test that the manufacturer’s claim is false.A) H0 µ ≤ .995 Ha µ > .995B) H0 µ ≠ 1 Ha µ = 1C) H0 µ ≥ 1 Ha µ < 1D) H0 µ = 1 Ha µ ≠ 1E) H0 µ ≤ 1 Ha µ > 1Answer: D Difficulty: Medium

184. Calculate the test statisticA) -2.83B) -1.41C) -2.00D) 2.83E) 1.41Answer: B Difficulty: Medium

185. Calculate the p-valueA) .0793B) .1586C) .0023D) .0046E) .0456Answer: B Difficulty: Medium


186. How much evidence do we have that the manufacturer’s claim is false?A) No evidenceB) Some evidenceC) Strong evidenceD) Very Strong evidenceE) Extremely Strong evidenceAnswer: A Difficulty: Easy

187. Calculate a confidence interval to test the hypotheses at α = .001.A) [0.987 1.003]B) [0.986 1.004]C) [0.984 1.006]D) [0.983 1.007]E) [0.988 1.002]Answer: D Difficulty: Medium

Use the following information to answer questions 188-192:The quality control manager at a cell phone battery factory needs to determine whether the mean life of a large shipment of batteries is equal to the specified value of 375 hours. The process standard deviation is known to be 100 hours. A random sample of 64 batteries indicates a sample mean of 350 hours

188. State the null and alternative hypotheses to test whether the shipment meets the specified value.A) H0 µ ≥ 350 Ha µ < 350B) H0 µ ≠ 375 Ha µ = 375C) H0 µ = 375 Ha µ ≠ 375D) H0 µ ≥ 375 Ha µ < 375E) H0 µ ≤ 375 Ha µ > 375Answer: C Difficulty: Medium

189. Calculate the test statisticA) -16.00B) -4.00C) -2.00D) 2.00E) 4.00Answer: C Difficulty: Medium


190. Calculate the p-valueA) 0.0001B) 0.0002C) 0.0228D) 0.0456E) -0.0228Answer: D Difficulty: Medium

191. How much evidence do we have that the shipment is meeting the specified value?A) No evidenceB) Some evidenceC) Strong evidenceD) Very Strong evidenceE) Extremely Strong evidenceAnswer: C Difficulty: Easy

192. Calculate a confidence interval to test the hypotheses at α = .01A) [317.8 382.2]B) [308.9 391.1]C) [311.4 362.5]D) [312.5 387.5]E) [320.9 379.1]Answer: A Difficulty: Medium

Use the following information to answer questions 193-197:An injector molder produces plastic pens. The process is designed to produce pens with a mean weight of 0.250 ounce. To investigate whether the injection molder is operating satisfactorily, 40 pens were randomly sample with a mean of 0.2525 and a standard deviation of .0022.

193. Set up the appropriate hypotheses to test that the process is performing satisfactorily.A) H 0 µ ≥ 0.250 Ha µ < 0.250B) H 0 µ = 0.250 Ha µ ≠ 0.250C) H 0 µ ≤ 0.250 Ha µ > 0.250D) H 0 µ ≠ 0.250 Ha µ = 0.250E) H 0 µ ≤ 0.2525 Ha µ > 0.2525Answer: B Difficulty: Medium


194. Calculate the test statisticA) 7.187B) .337C) 3.371D) -.337E) -7.187Answer: A Difficulty: Medium

195. What is the rejection point for α = .001 to test this hypothesis.A) 2.575B) 2.33C) 3.09D) 1.96E) 3.29Answer: E Difficulty: Medium

196. How much evidence do we have that the process is out of controlA) No evidenceB) Some evidenceC) Strong evidenceD) Very Strong evidenceE) Extremely Strong evidenceAnswer: E Difficulty: Medium

197. Calculate a confidence interval to test the hypotheses at α = .01A) [.2514 .2536]B) [.2516 .2534]C) [.2517 .2533]D) [.2518 .2532]E) [.2521 .2529]Answer: B Difficulty: Medium

Use the following information to answer questions 198-202:A survey of professors in History across the US found that the average income is $74,914. Since this survey is now over 8 years old, suppose an institutional researcher wants to test this figure by taking a random sample of 112 History professors. She finds a sample mean of $81,342 and a standard deviation of 15,121.


198. Set up the null and alternative hypotheses to determine is the figure has changed.A) H0 µ = 74914 Ha µ ≠ 74914B) H 0 µ ≥ 74914 Ha µ < 74914C) H 0 µ ≤ 74914 Ha µ > 74914D) H 0 µ ≠ 74914 Ha µ = 74914E) H 0 µ ≤ 81342 Ha µ > 81342Answer: A Difficulty: Medium

199. Calculate the test statisticA) 4.50B) 47.61C) 9.00D) -47.61E) -4.50Answer: A Difficulty: Medium

200. What is the rejection point for testing these hypotheses at α = .05.A) 1.28B) 1.645C) 1.96D) 2.33E) 2.575Answer: C Difficulty: Medium

201. How much evidence do we have that the figure has changed?A) No evidenceB) Some evidenceC) Strong evidenceD) Very Strong evidenceE) Extremely Strong evidenceAnswer: E Difficulty: Easy

202. Calculate a confidence interval to test the hypotheses at α = .001A) [79,539 83,145]B) [78,992 83,692]C) [76,640 86,044]D) [76,927 85,757]E) [77,661 85,023]Answer: C Difficulty: Medium


Use the following information to answer questions 203-207:It has been hypothesized that on average employees spend one hour a day playing video games at work. To test this at her company, a manager takes a random sample of 35 employees who showed a mean time of 55 minutes per day with a standard deviation of 5 minutes.

203. Set up the null and alternative hypothesis to test the claim that the company’s playing time differs from the national average.A) H0 µ ≤ 60 Ha µ > 60B) H0 µ ≥ 60 Ha µ< 60C) H0 µ = 55 Ha µ ≠ 55D) H0 µ = 60 Ha µ ≠ 60E) H0 µ ≠ 60 Ha µ = 60Answer: D Difficulty: Medium

204. Calculate the test statistic A) 5.92B) 63.89C) 11.84D) -5.92E) -63.89Answer: D Difficulty: Medium

205. What is the rejection point for testing these hypotheses at α = .01.A) 1.28B) 1.645C) 1.96D) 2.33E) 2.575Answer: E Difficulty: Medium

206. How much evidence do we have that this company’s employees are different from the average national employee?A) No evidenceB) Some evidenceC) Strong evidenceD) Very Strong evidenceE) Extremely Strong evidenceAnswer: E Difficulty: Easy


207. Calculate a confidence interval to test the hypotheses at α = .02.A) [52.39 57.61]B) [53.03 56.97]C) [52.82 57.18]D) [53.34 56.66]E) [52.46 57.54]Answer: B Difficulty: Medium

Use the following to answer questions 208-212:A cereal manufacturer is concerned that the boxes of cereal not be under filled or overfilled. Each box of cereal is supposed to contain 13 ounces of cereal. A random sample of 31 boxes is tested. The average weight is 12.58 ounces and the standard deviation is 0.25 ounces.

208. Setup the null and alternative hypothesis to test if the average number of ounces is different from 13 ounces.A) H0 µ ≥ 13 Ha µ < 13B) H0 µ = 13 Ha µ ≠ 13C) H0 µ ≤ 13 Ha µ > 13D) H0 µ ≠ 13 Ha µ = 13E) H0 µ ≤ 12.58 Ha µ > 12.58Answer: B Difficulty: Medium

209. Calculate the test statistic to test these hypothesesA) 9.35B) -9.35C) 4.68D) -4.68E) -1.68Answer: B Difficulty: Medium

210. What is the rejection point for testing these hypotheses at α = .001.A) 1.28B) 1.645C) 2.575D) 3.09E) 3.291Answer: E Difficulty: Medium


211. How much evidence do we have that the mean of the process is not 13 ounces?A) No evidenceB) Some evidenceC) Strong evidenceD) Very Strong evidenceE) Extremely Strong evidenceAnswer: E Difficulty: Easy

212. Calculate a confidence interval to test the hypotheses at α = .10A) [12.46 12.70]B) [12.48 12.68]C) [12.49 12.67]D) [12.51 12.65]E) [12.52 12.64]Answer: D Difficulty: Medium

Use the following information to answer questions 213-217:A new manufacturing method has been introduced to streamline the canning process of cherries. Although the time to fill a can has been reduced the quality control manager is concerned about the uniformity of the amount of cherries in each can. The cans are labeled to contain 14.5 ounces of cherries and natural juice. To be sure that this level has not been affected by the new method the manager randomly samples 80 cans over an eight hour shift. The mean number of ounces is 14.64 with a standard deviation of .4 ounces.

213. Set up the null and alternative hypothesis to determine if the new method has changed the amount of cherries that should be in the can.A) H0 µ ≥ 14.64 Ha µ ≤ 14.64B) H0 µ ≤ 14.5 Ha µ > 14.5C) H0 µ ≥ 14.5 Ha µ < 14.5D) H0 µ = 14.5 Ha µ ≠ 14.5E) H0 µ ≠ 14.5 Ha µ = 14.5Answer: D Difficulty: Medium

214. Calculate the test statisticA) 3.13B) 1.98C) 3.96D) -3.13E) -1.98Answer: A Difficulty: Medium


215. What is the rejection point for testing the hypotheses at α = .01.A) 3.09B) 3.29C) 2.33D) 2.575E) 1.96Answer: D Difficulty: Medium

216. How much evidence is there that the cans contain 14.5 ounces of cherries and juice?A) No evidenceB) Some evidenceC) Strong evidenceD) Very Strong evidenceE) Extremely Strong evidenceAnswer: D Difficulty: Easy

217. Calculate a confidence interval to test the hypotheses at α = .05A) [14.58 14.70]B) [14.57 14.71]C) [14.55 14.73]D) [14.54 14.74]E) [14.50 14.78]Answer: C Difficulty: Medium

Use the following information to answer questions 218-222:The local pharmacy prides itself on the accuracy of the number of tablets that are dispensed in a 60 count prescription. The new manager feels that the pharmacy assistants might have become careless in counting due to an increase in the volume of prescriptions. To test her theory she randomly selects 40 prescriptions requiring 60 tablets and recounts the number in each bottle. She finds a sample mean of 62.05 and a standard deviation of 4.45.

218. Set up the null and alternative hypothesis to test if the average number of tablets is different from the required number.A) H0 µ ≠ 60 Ha µ = 60B) H0 µ ≥ 40 Ha µ < 40C) H0 µ ≥ 60 Ha µ < 60D) H0 µ ≤ 60 Ha µ > 60E) H0 µ = 60 Ha µ ≠ 60Answer: E Difficulty: Medium


219. Calculate the test statisticA) 2.91B) -2.91C) -3.57D) 6.15E) 3.57Answer: A Difficulty: Medium

220. Calculate the p-valueA) 0.0000B) 0.0018C) 0.0036D) 0.0009E) 0.3859Answer: D Difficulty: Easy

221. How much evidence do we have to reject the null hypothesis?A) No evidenceB) Some evidenceC) Strong evidenceD) Very Strong evidenceE) Extremely Strong evidenceAnswer: D Difficulty: Easy

222. Calculate a confidence interval to test the hypotheses at α = .002A) [59.73 64.37]B) [59.88 64.22]C) [60.24 63.86]D) [60.67 63.43]E) [61.15 62.95]Answer: B Difficulty: Medium

Use the following information to answer questions 223-230:Last year, during an investigation of the time spent reading e-mails on a daily basis, researchers found that on Monday the average time was 50 minutes. Office workers claim that with the increased spam and junk mail, this time has now increased. To conduct a test, a sample of 25 employees is selected with the following results: sample mean = 51.05 minutes and sample standard deviation = 14.2 minutes.


223. Set up the null and alternative hypotheses to test the workers’ claim.A) HO: μ = 50 vs. HA: μ ≠ 50B) HO: μ ≥ 50 vs. HA: μ < 50C) HO: μ ≥ 51.05 vs. HA: μ < 51.05D) HO: μ ≠ 50 vs. HA: μ = 50E) HO: μ ≤ 50 vs. HA: μ > 50Answer: E Difficulty: Medium

224. Calculate the appropriate test statistic to test the hypotheses.A) 2.38B) 1.19C) -1.19D) 1.76E) -1.76Answer: B Difficulty: Medium

225. What is the rejection point for α = .05 to test the hypotheses.A) 1.711B) 2.064C) 2.060D) 1.708E) 1.645Answer: A Difficulty: Medium

226. How much evidence do we have that the workers’ claim is true?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: A Difficulty: Easy

Use the following information to answer questions 227-230:The manager of a local specialty store is concerned with a possible slowdown in payments by her customers. She measures the rate of payment in terms of the average number of days receivables are outstanding. Generally, the store has maintained an average of 50 days with a standard deviation of 10 days. A random sample of 25 accounts gives an average of 54 days outstanding with a standard deviation of 8 days.


227. Set up the null and alternative hypotheses needed to show that there has been a slowdown in payments by the company’s customers.A) HO: μ = 50 vs. HA: μ ≠ 50B) HO: μ ≥ 54 vs. HA: μ < 54C) HO: μ ≥ 50 vs. HA: μ < 50D) HO: μ ≠ 50 vs. HA: μ = 50E) HO: μ ≤ 50 vs. HA: μ > 50Answer: E Difficulty: Medium

228. Calculate the appropriate test statistic to test the hypotheses.A) -2.00B) -2.50C) 12.50D) 2.50E) 2.00Answer: D Difficulty: Medium

229. What is the rejection point for α = .01 to test the hypotheses.A) 2.485B) 2.797C) 2.492D) 2.787E) 2.327Answer: C Difficulty: Medium

230. How much evidence do we have that there is a slowdown?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: D Difficulty: Easy

Use the following information to answer questions 231-234:In research on cell phone use by teenagers it was found that the average connect time for a call was at least 15 minutes. Social psychologists feel that this study understated the time. To determine this claim, cell phone bills for 15 teenagers were evaluated. On average, the time spent was 18.5 minutes with a sample standard deviation of four minutes (assume a normal distribution).


231. Set up the null and alternative hypotheses to test whether the original research claim is valid,A) HO: μ = 15 vs. HA: μ ≠ 15B) HO: μ ≥ 15 vs. HA: μ < 15C) HO: μ ≥ 18.5 vs. HA: μ < 18.5D) HO: μ ≠ 15 vs. HA: μ = 15E) HO: μ ≤ 15 vs. HA: μ > 15Answer: E Difficulty: Medium

232. Calculate the appropriate test statistic to test the hypotheses.A) 3.39B) 13.125C) 0.875D) -0.875E) -3.39Answer: A Difficulty: Medium

233. What is the rejection point for α = .001 to test the hypotheses.A) 4.140B) -4.140C) 4.073D) 3.291E) 3.787Answer: E Difficulty: Easy

234. How much evidence do we have that cell phone conversations are longer than the original claim?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: D Difficulty: Medium

Use the following information to answer questions 235-238:The quality control manager of a major cell phone provider is concerned about the life of the cell phone batteries they use. He took a sample of 13 batteries from a recent shipment and used them continuously until they failed to work. The manager measured the number of hours the batteries lasted and found the mean to be 550.4 with a standard deviation of 315.3.


235. Set up the null and alternative hypotheses to provide evidence that the mean life of the batteries is more than 400 hours.A) HO: μ = 400 vs. HA: μ ≠ 400B) HO: μ ≥ 400 vs. HA: μ < 400C) HO: μ ≥ 550.4 vs. HA: μ < 550.4D) HO: μ ≠ 400 vs. HA: μ = 400E) HO: μ ≤ 400 vs. HA: μ > 400Answer: E Difficulty: Medium

236. Calculate the appropriate test statistic to test the hypotheses.A) 6.20B) 1.72C) 0.477D) -6.20E) -1.72Answer: B Difficulty: Medium

237. What is the rejection point for α = .10 to test the hypotheses.A) -1.356B) 1.356C) 1.282D) 1.782E) -1.782Answer: B Difficulty: Medium

238. How much evidence do we have that the mean life is more than 400 hours?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: B Difficulty: Medium

Use the following information to answer questions 239-242:The changing ecology of the swamps in Louisiana has been the subject of much environmental research. One water-quality parameter of concern is the total phosphorous level. Suppose that the EPA makes 15 measurements in one area of the swamp, yielding a mean level of total phosphorus of 12.3 parts per billion (ppb) and a standard deviation of 5.4 ppb. The EPA wants to test whether the data support the conclusion that the mean level is less than 15 ppb.


239. Set up the null and alternative hypotheses to test whether the standard is being metA) HO: μ = 15 vs. HA: μ ≠ 15B) HO: μ ≥ 15 vs. HA: μ < 15C) HO: μ ≥ 12.3 vs. HA: μ < 12.3D) HO: μ ≠ 15 vs. HA: μ = 15E) HO: μ ≤ 15 vs. HA: μ > 15Answer: B Difficulty: Medium (AS)

240. Calculate the appropriate test statistic to test the hypotheses.A) 7.50B) 1.94C) 3.88D) -7.50E) -1.94Answer: E Difficulty: Medium (AS)

241. What is the rejection point for α = .05 to test the hypotheses.A) -1.761B) -1.753C) -2.145D) 1.645E) 2.132Answer: A Difficulty: Easy (AS)

242. How much evidence do we have that the mean level of phosphorus is less than 15 parts per billion?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: B Difficulty: Easy (AS)

Use the following information to answer questions 243-246:In a bottling process, a manufacturer will lose money if the bottles contain either more or less than is claimed on the label. Suppose a quality manager for a steak sauce company is interested in testing whether the mean number of ounces of steak sauce per restaurant size bottle differs from the labeled amount of 20 ounces. The manager samples nine bottles, measures the weight of their contents, and finds the sample mean is 19.7 ounces and the sample standard deviation is 0.3 ounces.


243. Set up the null and alternative hypotheses to test the quality manager’s claim.A) HO: μ = 20 vs. HA: μ ≠ 20B) HO: μ ≥ 20 vs. HA: μ < 20C) HO: μ ≥ 19.7 vs. HA: μ < 19.7D) HO: μ ≠ 20 vs. HA: μ = 20E) HO: μ ≤ 20 vs. HA: μ > 20Answer: A Difficulty: Medium

244. Calculate the appropriate test statistic to test the hypotheses.A) 3.00B) 1.00C) -9.00D) -1.00E) -3.00Answer: E Difficulty: Medium

245. What is the rejection point for α = .05 to test the hypotheses.A) 2.306B) 2.262C) 1.860D) 3.09E) 1.96Answer: A Difficulty: Easy

246. How much evidence do we have to reject the null hypothesis?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: C Difficulty: Easy

Use the following information to answer questions 247-250:A major car manufacturer wants to test a new catalytic converter to determine whether it meets new air pollution standards. The mean emission of all converters of this type must be less than 20 parts per million of carbon. Ten (10) converters are manufactured for testing purposes and their emission levels are measured with a mean of 17.17 and a standard deviation of 2.98.


247. Set up the null and alternative hypotheses to support the claim that the mean emission level for all converters of this type is less than 20 ppm.A) HO: μ = 20 vs. HA: μ ≠ 20B) HO: μ ≥ 20 vs. HA: μ < 20C) HO: μ ≥ 17.17 vs. HA: μ < 17.17D) HO: μ ≠ 20 vs. HA: μ = 20E) HO: μ ≤ 20 vs. HA: μ > 20Answer: B Difficulty: Medium

248. Calculate the appropriate test statistic to test the hypotheses.A) 3.00B) 9.50C) -0.95D) -3.00E) -9.50Answer: D Difficulty: Medium

249. What is the rejection point for α = .01 to test the hypotheses.A) -2.821B) -3.250C) -2.33D) 2.821E) 3.250Answer: A Difficulty: Easy

250. How much evidence do we have that the new catalytic converter type meets the pollution standard?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: D Difficulty: Easy

Use the following information to answer questions 251-254:According to a national survey, the average commuting time for people who commute to a city with a population of 1 to 3 million is 19.0 minutes. Suppose a researcher lives in a city with a population of 2.4 million and wants to test this claim in her city. Taking a random sample of 20 commuters she calculates a mean time of 19.346 minutes and a standard deviation of 2.842 minutes.


251. Set up the null and alternative hypotheses to test the claim.A) HO: μ = 19 vs. HA: μ ≠ 19B) HO: μ ≥ 19 vs. HA: μ < 19C) HO: μ ≥ 20 vs. HA: μ < 20D) HO: μ ≠ 19 vs. HA: μ = 19E) HO: μ ≤ 19 vs. HA: μ > 19Answer: A Difficulty: Medium

252. Calculate the appropriate test statistic to test the hypotheses.A) 1.08B) 0.54C) -1.08D) -0.54E) 3.60Answer: B Difficulty: Medium


254. How much evidence do we have to reject the null hypothesis?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: A Difficulty: Easy

Use the following information to answer questions 255-258:In 1930, the average size of a public restroom was 172 square feet; by 1990, due to federal disability laws, the average size had increased to 471 square feet. Suppose that a design team believes that this standard has increased from the 1990 level. They randomly sample 23 public restrooms in a major Midwestern city and obtain a mean square footage of 498.78 with a standard deviation of 46.94.


255. Set up the null and alternative hypotheses for the designer’s claim that the size had increased from the 1990 level.A) HO: μ = 471 vs. HA: μ ≠ 471B) HO: μ ≥ 471 vs. HA: μ < 471C) HO: μ ≥ 174 vs. HA: μ < 174D) HO: μ ≠ 471 vs. HA: μ = 471E) HO: μ ≤ 471 vs. HA: μ > 471Answer: E Difficulty: Medium (AS)

256. Calculate the appropriate test statistic to test the hypotheses.A) 2.84B) 13.61C) 30.34D) -2.84E) -13.61Answer: A Difficulty: Medium (AS)

257. What is the rejection point for α = .001 to test the hypotheses.A) 3.792B) 3.767C) 3.505D) 3.485E) 3.09Answer: C Difficulty: Medium (AS)

258. How much evidence do we have that the designer’s claim is true?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: D Difficulty: Easy (AS)

Use the following to answer questions 259-262:A manufacturing operation consists of a unique system that produces an average of 15.5 jet engine propulsion parts every hour. After undergoing a complete overhaul, the system was monitored by observing the number of parts produced in each of seventeen randomly selected one-hour periods. The mean is 15.42 with a standard deviation of 0.16.


259. Set up the null and alternative hypotheses to test whether the number of parts produced by the overhauled system differs from 15.5.A) HO: μ = 15.5 vs. HA: μ ≠ 15.5B) HO: μ ≥ 15.5 vs. HA: μ < 15.5C) HO: μ ≥ 15.42 vs. HA: μ < 15.42D) HO: μ ≠ 15.5 vs. HA: μ = 15.5E) HO: μ ≤ 15.5 vs. HA: μ > 15.5Answer: A Difficulty: Medium

260. Calculate the appropriate test statistic to test the hypotheses.A) -0.50B) -2.06C) -8.50D) 0.50E) 2.06Answer: B Difficulty: Medium


262. How much evidence do we have that the system differs from 15.5?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: B Difficulty: Easy

Use the following to answer questions 263-266:A sample of 400 journalism majors at a major research university were asked if they agreed with the following statement “Government should be more involved in oversight and regulation of reporting”. Fifty-two (52) percent of the respondents agreed with the statement.


263. Set up the appropriate hypotheses that attempt to provide evidence supporting the claim that at least 50% journalism majors agree with the statement.A) H0: ρ ≤ .52 vs HA: ρ > .52B) H0: ρ ≥ .50 vs HA: ρ < .50C) H0: ρ ≤ .50 vs HA: ρ > .50D) H0: ρ = .50 vs HA: ρ ≠ .50E) H0: ρ ≠ .50 vs HA: ρ = .50Answer: C Difficulty: Medium

264. Calculate the appropriate test statistic to test the hypotheses.A) 0.80B) 1.60C) 8.00D) -1.60E) -0.80Answer: A Difficulty: medium

265. Calculate the p-value associated with the test statistic.A) .0001B) .2000C) .2119D) .2881E) .4238Answer: C Difficulty: Medium

266. How much evidence do we have to reject the null hypothesis in favor of the alternative hypothesis that the percent agreeing with the statement is more than 50%?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: A Difficulty: Easy

Use the following to answer questions 267-270:In an early study, researchers at an Ivy University found that 33% of the freshmen had received at least one A in their first semester. Administrators are concerned that grade inflation has caused this percentage to increase. In a more recent study, of a random sample of 500 freshmen, 185 had at least one A in their first semester.


267. Set up the appropriate hypotheses that attempt to test the claim that the proportion of of freshmen receiving at least one A is now greater than one-third (.33).A) H0: ρ ≤ .37 vs HA: ρ > .37B) H0: ρ ≥ .33 vs HA: ρ < .33C) H0: ρ ≤ .33 vs HA: ρ > .33D) H0: ρ = .33 vs HA: ρ ≠ .33E) H0: ρ ≠ .33 vs HA: ρ = .33Answer: C Difficulty: Medium

268. Calculate the appropriate test statistic to test the hypotheses.A) 1.853B) 1.157C) 1.902D) 2.710E) -1.902Answer: C Difficulty: Medium

269. Calculate the p-value associated with the test statistic.A) .0034B) .0287C) .0322D) .0547E) .1230Answer: B Difficulty: Medium

270. How much evidence do we have to reject the null hypothesis in favor of the alternative hypothesis that the percent receiving at least one A is now greater than one third?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: C Difficulty: Easy

Use the following to answer questions 271-274:In a survey conducted of 1000 workers by Employeesavings.com in August 2000, 440 indicated that they have Internet access at work (Carlos Tejada, “Work Week”, Wall Street Journal, August 29,2000, A1)


271. Set up the appropriate hypotheses that attempt to provide evidence supporting the claim that fewer than half (.50) of the employed workers in the US have Internet access at work.A) H0: ρ ≤ .44 vs HA: ρ > .44B) H0: ρ ≥ .50 vs HA: ρ < .50C) H0: ρ ≤ .50 vs HA: ρ > .50D) H0: ρ = .50 vs HA: ρ ≠ .50E) H0: ρ ≠ .50 vs HA: ρ = .50Answer: B Difficulty: Medium

272. Calculate the appropriate test statistic to test the hypotheses.A) 3.82B) 3.79C) 2.52D) -2.54E) -3.79Answer: E Difficulty: Medium

273. Calculate the p-value associated with the test statistic.A) -0.0001B) 0.0001C) 0.0055D) 0.0059E) 0.4990Answer: B Difficulty: Easy

274. How much evidence do we have to reject the null hypothesis in favor of the alternative hypothesis that fewer than half of the employed workers in the US have Internet access at work?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: E Difficulty: Easy

Use the following to answer questions 275-278:The university registrar claims that fewer than 20 percent of the students who enroll at Ivy University graduate in four years. To test this claim, a random sample of 100 students was selected, and 18 were found to have graduated in four years.


275. Set up the appropriate hypotheses that attempt to provide evidence supporting the claim that at least 50% of college-educated 35 to 64 year-olds with incomes more than $100,000 agree with the statement.A) H0: ρ ≤ .18 vs HA: ρ > .18B) H0: ρ ≥ .20 vs HA: ρ < .20C) H0: ρ ≤ .20 vs HA: ρ > .20D) H0: ρ = .20 vs HA: ρ ≠ .20E) H0: ρ ≠ .20 vs HA: ρ = .20Answer: B Difficulty: Medium

276. Calculate the appropriate test statistic to test the hypotheses.A) 5.00B) 0.50C) 0.212D) -0.50E) -1.00Answer: D Difficulty: Medium

277. Calculate the p-value associated with the test statistic.A) 0.1587B) 0.3085C) 0.4168D) 0.0001E) -0.3085Answer: B Difficulty: Easy

278. How much evidence do we have to reject the null hypothesis in favor of the alternative hypothesis that the graduation rate is less than 20 percent?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: A Difficulty: Easy

Use the following to answer questions 279-282:Last year, KAAA’s share of the 6 pm news audience was approximately equal to, but not greater than, 25 percent. This station’s advertising department believes the current audience share is higher than last year’s 25 percent share. In an attempt to substantiate this belief, the station surveyed a random sample of 400 6 pm viewers and found that 146 watched KAAA.


279. Set up the appropriate hypotheses to test the advertising department’s claim.A) H0: ρ ≤ .365 vs. HA: ρ > .365B) H0: ρ ≥ .250 vs. HA: ρ < .250C) H0: ρ ≤ .250 vs. HA: ρ > .250D) H0: ρ = .250 vs. HA: ρ ≠ .250E) H0: ρ ≠ .250 vs. HA: ρ = .250Answer: C Difficulty: Medium (AS)

280. Calculate the appropriate test statistic to test the hypotheses.A) -5.31B) -4.69C) 3.21D) 4.69E) 5.31Answer: E Difficulty: Medium (AS)

281. Find the rejection point for testing these hypotheses at α = .001.A) 3.09B) 2.575C) 2.33D) 1.96E) 3.00Answer: A Difficulty: Easy (AS)

282. How much evidence do we have that the current audience share is higher than last year’s 25 percent share?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: E Difficulty: Easy (AS)

Use the following information to answer questions 283-287:Failure to meet payments on student loans guaranteed by the US government has been a major problem for both banks and the government. Approximately 50% of all student loans guaranteed by the government are in default. A random sample of 350 loans to college students in one region of the US indicates that 147 are in default.


283. Set up the appropriate hypotheses that attempt to provide evidence supporting the claim that at least 50% of college-educated 35 to 64 year-olds with incomes more than $100,000 agree with the statement.A) H0: ρ ≤ .42 vs HA: ρ > .42B) H0: ρ ≥ .50 vs HA: ρ < .50C) H0: ρ ≤ .50 vs HA: ρ > .50D) H0: ρ = .50 vs HA: ρ ≠ .50E) H0: ρ ≠ .50 vs HA: ρ = .50Answer: D Difficulty: Medium

284. Calculate the appropriate test statistic to test the hypotheses.A) 2.99B) 3.03C) -2.99D) -3.03E) -1.94Answer: C Difficulty: Medium

285. Calculate the p-value associated with the test statistic.A) .0028B) .0262C) .0525D) .0014E) .0012Answer: A Difficulty: Easy

286. How much evidence do we have that the region differs from the national population?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: D Difficulty: Easy

287. Calculate an interval that tests the hypotheses at α = .01.A) [.35 .49]B) [.37 .47]C) [.33 .51]D) [.34 .50]E) [.36 .48]Answer: A Difficulty: Medium


Use the following information to answer questions 288-292:Sleep researchers theorize that 25% of the general population suffers from obstructive sleep apnea. Researchers found that 124 of 159 emergency room nurses suffered from obstructive sleep apnea.

288. Set up the appropriate hypotheses that attempt to provide that emergency room nurses differ from the general population proportion.A) H0: ρ ≤ .780 vs HA: ρ > .780B) H0: ρ ≥ .250 vs HA: ρ < .250C) H0: ρ ≤ .250 vs HA: ρ > .250D) H0: ρ = .250 vs HA: ρ ≠ .250E) H0: ρ ≠ .250 vs HA: ρ = .250Answer: D Difficulty: Medium

289. Calculate the appropriate test statistic to test the hypotheses.A) -16.13B) -15.43C) 13.63D) 15.43E) 16.13Answer: E Difficulty: Medium

290. Find the rejection point to test the hypotheses at α = .001.A) 1.645B) 1.960C) 2.575D) 3.090E) 3.291Answer: E Difficulty: Easy

291. How much evidence do we have to reject the null hypothesis in favor of the alternative hypothesis that nurses differ from the general population?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: E Difficulty: Easy


292. Calculate an interval to test the hypotheses at α = .001.A) [.14 .36]B) [.17 .33]C) [.67 .89]D) [.68 .88]E) [.70 .86]Answer: C Difficulty: Medium

Use the following information to answer questions 293-296:A survey of the wine market has shown that the preferred wine for 17% of Americans is merlot. A wine producer in California where merlot is produced believes the figure is higher in California. She contacts a random sample of 550 California residents and asks which wine they purchase most often. Suppose 115 replied that merlot was the primary wine.

293. Set up the appropriate hypotheses to test the wine producer’s claim.A) H0: ρ ≤ .21 vs HA: ρ > .21B) H0: ρ ≥ .17 vs HA: ρ < .17C) H0: ρ ≤ .17 vs HA: ρ > .17D) H0: ρ = .17 vs HA: ρ ≠ .17E) H0: ρ ≠ .17 vs HA: ρ = .17Answer: C Difficulty: Medium (AS)

294. Calculate the appropriate test statistic to test the hypotheses.A) 2.25B) 2.44C) 1.11D) -2.25E) -2.44Answer: B Difficulty: Medium (AS)

295. Calculate the p-value associated with the test statistic.A) .0146B) .0122C) .0073D) .1335E) .0244Answer: C Difficulty: Easy (AS)


296. How much evidence do we have to reject the null hypothesis in favor of the alternative hypothesis that California residents purchase merlot at a higher percentage that the national percentage?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: D Difficulty: Easy (AS)

Use the following information to answer questions 297-301:One survey conducted by a major leasing company determined that the Lexus is the favorite luxury car for 25% of leases in Atlanta. Suppose a US car manufacturer conducts its own survey in an effort to determine if this figure is correct. Of the 384 leases in Atlanta surveyed, 79 lease a Lexus.

297. Set up the appropriate hypotheses to test whether the claim is true.A) H0: ρ ≤ .210 vs. HA: ρ > .210B) H0: ρ ≥ .250 vs. HA: ρ < .250C) H0: ρ ≤ .250 vs. HA: ρ > .250D) H0: ρ = .250 vs. HA: ρ ≠ .250E) H0: ρ ≠ .250 vs. HA: ρ = .250Answer: D Difficulty: Medium

298. Calculate the appropriate test statistic to test the hypotheses.A) -2.15B) -2.00C) -0.91D) 2.00E) 2.51Answer: B Difficulty: Medium

299. Calculate the p-value associated with the test statistic.A) 0.0228B) 0.0456C) 0.1814D) 0.3628E) 0.4772Answer: B Difficulty: Easy


300. How much evidence do we have to reject the null hypothesis in favor of the alternative hypothesis?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: C Difficulty: Easy

301. Calculate a confidence interval that tests the hypotheses at α = .02.A) [.165 .246]B) [.179 .232]C) [.142 .269]D) [.153 .259]E) [.158 .254]Answer: E Difficulty: Medium

Use the following information to answer questions 302-305:If you live in California, the decision to buy earthquake insurance is an important one. A survey revealed that only 133 of 337 randomly selected residences in one California county were protected by earthquake insurance.

302. Set up the appropriate hypotheses to test the claim that less than 40 percent of the residents in this county are protected by earthquake insurance.A) H0: ρ ≤ .39 vs. HA: ρ > .39B) H0: ρ ≥ .40 vs. HA: ρ < .40C) H0: ρ ≤ .40 vs. HA: ρ > .40D) H0: ρ = .40 vs. HA: ρ ≠ .40E) H0: ρ ≠ .40 vs. HA: ρ = .40Answer: B Difficulty: Medium

303. Calculate the appropriate test statistic to test the hypotheses.A) 0.20B) 0.40C) -0.13D) -0.20E) -0.40Answer: D Difficulty: Medium


304. Calculate the p-value associated with the test statistic.A) 0.0793B) 0.1554C) 0.3446D) 0.4207E) 0.4483Answer: D Difficulty: Medium

305. How much evidence do we have to reject the null hypothesis in favor of the alternative hypothesis that less than 40% of the residents are protected by earthquake insurance?A) No evidenceB) Some evidenceC) Strong evidenceD) Very strong evidenceE) Extremely strong evidenceAnswer: A Difficulty: Easy


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Chapter 08 - Quiz