Download True/False Questions - ManagerialStatistics

Chapter 8
Hypothesis 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
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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
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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
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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
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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
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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
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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 X = 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 z
B) Less than -z
C) Greater than z/2
D) Greater than z
E) 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 < -z
C) z > z
D) p-value < 
E) Both B and D
Answer: E Difficulty: Medium
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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 Z
Answer: 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
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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
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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
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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
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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
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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
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Essay
77. Test H0:  ≤ 8 versus HA:  > 8, given  = .01, n = 25, X = 8.112, and s = .16. Assume
the sample is selected from a normally distributed population.
Answer: Reject H0
H0 :   8 H A :   8
8.112  8
 3.5
.16
25
t.01,24  2.492
t
3.5  2.492, reject H 0
Difficulty: Medium
78. Test H0:   22 versus HA:  < 22, given  = .01, n = 100, X = 21.431, and s = 1.295.
Answer: Reject H0
H 0 :   22 H A :   22
21.431  22 .569

 4.394
1.295
.1295
100
Z.01  2.33
Z
4.394  2.33, reject H 0
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
H 0 :   18
H A :   18
X  16, s  4.195
16  18
 1.167
4.195
6
t.025,5  2.571
t
1.167  2.571, failed to reject H 0
Difficulty: Hard
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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
X = .6419, s = .02049
.6419 - .625
t
 2.61
0.02049
10
t10,9 = 1.383
2.61 > 1,383, Reject H0
Difficulty: Hard
81. Determine the p-value for H0: p ≤ .5 versus HA: p > .5 when n = 225 and p̂ = .54.
Answer: .1151
.54  .5
Z
 1.2
(.5)(.5)
225
p  value  .5  .3849  .1151
Difficulty: Medium
82. Determine the p-value for H0: p = .5 versus HA: p  .5 when n = 225 and p̂ = .54.
Answer: .2302
.54  .5
Z
 1.2
(.5)(.5)
225
p  value  2(.5  .3849)  .2302
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
4.8
Z

 2.94
9.92
1.6308
37
p  value  .5  .4984  .0016
Difficulty: Medium
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84. Determine the p-value for H0:  = 95 versus HA:   95 when X = 90.2, s = 9.92, and n =
37.
Answer: .0032
90.2  95
4.8
Z

 2.94
9.92
1.6308
37
p  value  2(.5  .4984)  .0032
Difficulty: Medium
85. Test H0:  = 32 versus HA:  > 32 when X = 36, s = 1.6, and n = 30 at  = .05.
Answer: Reject H0
H 0 :   32 H A :   32
36  32
 13.693
1.6
30
t.05,29  1.699
t
13.693  1.699, reject H 0 .
Difficulty: Medium
86. In testing H0:  = 23 versus HA:  > 23 when X =26, s = 6, and n = 20, what is the value of
the t-statistic?
Answer: 2.24
26  23
t
 2.24
6
20
Difficulty: Easy
87. In testing H0:  ≤ 23 versus HA:  > 23 when X = 26, s = 6, and n = 30, what is the value
of the z-statistic?
Answer: 2.74
26  23
Z
 2.74
6
30
Difficulty: Easy
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88. In testing H0: p = .2 versus HA: p  .2 with p̂ = .26 and n = 100, what is the value of the zstatistic?
Answer: 1.5
.26  .2
Z
 1.5
(.2)(.8)
100
Difficulty: Easy
89. Test H0: p = .2 versus HA: p  .2 with p̂ = .26 and n = 100 at alpha = .05.
Answer: Fail to reject H0
H 0 : p  .2 H A : p  .2
Z
Z.025
.26  .2
 1.5
(.2)(.8)
100
 1.96
1.5  1.96, failed to reject H 0
Difficulty: Medium
90. In testing H0: p  .33 versus HA: p < .33 with p̂ = .20 and n = 100, what is the value of the
z-statistic?
Answer: -2.77
.2  .33
Z
 2.77
(.33)(.67)
100
Difficulty: Medium
91. Test at  = .05 H0: p = .33 versus HA: p < .33 with p̂ = .20 and n = 100.
Answer: Reject H0
H 0 : p  .33 H A : p  .33
Z
 Z.05
.2  .33
 2.77
(.33)(.67)
100
 1.645
2.77  1.645, reject H 0
Difficulty: Medium
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92. Test H0:  ≤ .95 versus HA:  > .95 when X = .99, s = .12, and n = 24 at alpha = .05.
Assume a normally distributed population.
Answer: Reject H0
H 0 :   .95 H A :   .95
.99  .95
 1.633
.12
24
t.05,23  1.714
t
1.633  1.714, failed to reject H 0 .
Difficulty: Medium
93. Test H0: p  .7 versus HA: p < .7 with p̂ = .63 and n = 100 at  = .01.
Answer: Fail to reject H0
H 0 : p  .7 H A : p  .7
.63  .7
 1.53
(.7)(.3)
100
 Z.01  2.33
Z
1.53  2.33, we failed to reject H 0
Difficulty: Medium
94. Test H0:  ≤ 3.0 versus HA:  > 3.0 when X = 3.44, s = .57, and n = 13 at a significance
level of .05. Assume population normality.
Answer: Reject H0
H0 :   3 H A :   3
3.44  3.0
 2.783
.57
13
t.05,12  1.782
t
2.783  1.782, reject H 0 .
Difficulty: Medium
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95. Test H0:   2.5 versus HA:  < 2.5 when X = 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
H 0 :   2.5 H A :   2.5
2.46  2.5
 4.08
.05
26
t.10,25  1.318
t
4.08  1.318, reject H 0 .
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.
H 0 : p  .5 H A : p  .5
270
 .54
500
.54  .50
Z
 1.789
(.5)(.5)
500
Z.05  1.645
pˆ 
1.789  1.645, we reject H 0
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
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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.
H0 :   3 H A :   3
2.79  3
 1.954
.76
50
 Z.01  2.33
Z
1.954  2.33, we failed to reject H 0 .
Difficulty: Medium
Use the following information to answer questions 99-106
A 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  26
Z
 2.5
4
100
Difficulty: Medium (AS)
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245
104. What is the decision at  = .05?
Answer: Reject H0
27  26
Z
 2.5
4
100
2.5 > 1.645, therefore, reject H0.
Difficulty: Medium (AS)
105. What is the decision at  = .01?
Answer: Reject H0
27  26
Z
 2.5
4
100
2.5 > 2.33, therefore, reject H0.
Difficulty: Medium (AS)
106. What is the p-value for this test?
Answer: .0062
27  26
Z
 2.5
4
100
p  value  .5  .4938  .0062
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
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109. What is the rejection point (given in terms of the value of the test statistic) at  = .05?
Answer: t = 1.711
t24, 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 = 2.492
t24, 01 = 2.492 Difficulty: Medium
111. What is the sample value of the test statistic?
Answer: t = 1.0
102  100
Z
1
10
25
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
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247
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
1020
pˆ 
 .68
1500
.68  .66
Z
 1.635
(.66)(.34)
1500
Difficulty: Medium
120. What is the decision at  = .10?
Answer: Reject H0
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
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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.
H0 :   6 H A :   6
6.5  6
 2
1.5
36
t.10,35  1.30 or 1.31 reject H 0
Difficulty: Medium
t
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
199
198
176
180
174
181
183
208
188
198
165
Answer: Average assembly time is not equal to 3 minutes.
H 0 :   180 H A :   180
X  186.67
s  12.471
t.05,11  1.796
186.67  180
 1.852
12.471
12
1.852  1.796, reject H 0
Difficulty: Medium
tcalc 
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249
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
 .4 
2.4  1.75 
  2.225
 16 
2.225  2.125
Z
1
.1
P(2.125    2.225)  .3413
  .5  .3413  .1587
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:
 .4 
2.4  1.75 
  2.225
 16 
2.225  2.125
Z
1
.1
P (2.125    2.225)  .3413
  .5  .3413  .1587
Power  1    1  .1587  .8413
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.
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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
 .4 
2.4  1.75 
  2.225
 16 
2.225  2.175
Z
 .50
.1
P (2.125    2.175)  .1915
  .5  .1915  .3085
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
 .4 
2.4  1.75 
  2.225
 16 
2.225  2.175
Z
 .50
.1
P(2.125    2.175)  .1915
  .5  .1915  .3085
Power  1  .3085  .6915
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
 .36 
2.4  1.645 
  2.3013
 36 
2.3013  2.175
Z
 2.9353
.06
P (2.125    2.3013)  .4984
  .5  .4984  .0016
Difficulty: Hard
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251
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
 .36 
2.4  1.645 
  2.3013
 36 
2.3013  2.175
Z
 2.9353
.06
P(2.125    2.3013)  .4984
  .5  .4984  .0016
Power  1  .0016  .9984
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
 (1.645  2.05)(.36)
n
2
(2.4  2.2) 2
Difficulty: Hard
 44.23  45
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
(1.96  2.33)(.40) 

n
 130.874  131
(2.4  2.25) 2
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.
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133. Set up the null and alternative hypotheses to test whether the standard is being met
A) HO: μ = 6 vs. HA: μ ≠ 6
B) HO: μ ≥ 6.65 vs. HA: μ < 6.65
C) HO: μ ≥ 6 vs. HA: μ < 6
D) HO: μ ≠ 6 vs. HA: μ = 6
E) HO: μ ≤ 6 vs. HA: μ > 6
Answer: C Difficulty: Medium
134. Calculate the appropriate test statistic to test the hypotheses.
A) 2.71
B) 16.90
C) 0.65
D) -2.71
E) 3.31
Answer: A Difficulty: Medium
135. What is the rejection point for α = .10 to test the hypotheses.
A) -1.28
B) -1.96
C) -2.33
D) 1.28
E) 1.96
Answer: C Difficulty: Easy
136. How much evidence do we have that the standard is being met?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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.
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253
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 ≠ 7.5
B) HO: μ ≥ 7.5 vs. HA: μ < 7.5
C) HO: μ ≥ 8.1 vs. HA: μ < 8.1
D) HO: μ ≠ 7.5 vs. HA: μ = 7.5
E) HO: μ ≤ 7.5 vs. HA: μ > 7.5
Answer: E Difficulty: Medium (AS)
138. Calculate the appropriate test statistic to test the hypotheses.
A) -4.13
B) 36.92
C) 4.71
D) -4.71
E) 4.13
Answer: E Difficulty: Medium (AS)
139. What is the rejection point for α = .001 to test the hypotheses.
A) 2.575
B) 3.09
C) -1.96
D) -2.575
E) -3.09
Answer: B Difficulty: Easy (AS)
140. How much evidence do we have that the time is longer than 7.5 days?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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.
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141. Set up the null and alternative hypotheses to test the manufacturer’s claim
A) HO: μ = 3.3 vs. HA: μ ≠ 3.3
B) HO: μ ≥ 3.5 vs. HA: μ < 3.5
C) HO: μ ≥ 3.3 vs. HA: μ < 3.3
D) HO: μ ≠ 3.5 vs. HA: μ = 3.5
E) HO: μ ≤ 3.5 vs. HA: μ > 3.5
Answer: B Difficulty: Medium
142. Calculate the appropriate test statistic to test the hypotheses.
A) 1.29
B) 9.09
C) -1.29
D) -2.58
E) -9.09
Answer: C Difficulty: Medium
143. Calculate the p-value that corresponds to the test statistic.
A) 0.0985
B) 0.0001
C) 0.4015
D) 0.005
E) -0.985
Answer: A Difficulty: Medium
144. How much evidence do we have that the claim is true?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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 lifetime 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.
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255
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 ≠ 1502.5
B) HO: μ ≥ 1511.4 vs. HA: μ < 1511.4
C) HO: μ ≥ 1502.5 vs. HA: μ < 1502.5
D) HO: μ ≠ 1502.5 vs. HA: μ = 1502.5
E) HO: μ ≤ 1502.5 vs. HA: μ > 1502.5
Answer: E Difficulty: Medium
146. Calculate the appropriate test statistic to test the hypotheses.
A) 56.09
B) 3.74
C) 22.34
D) -3.74
E) -22.34
Answer: B Difficulty: Medium
147. What is the rejection point for α = .05 to test the hypotheses.
A) 1.645
B) -1.645
C) 1.96
D) 1.28
E) -1.96
Answer: A Difficulty: Easy
Refer To: 08_13
148. How much evidence do we have that the new cartridge is better than the old?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: E Difficulty: Easy
Refer 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.
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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 ≠ 10
B) HO: μ ≥ 10.94 vs. HA: μ < 10.94
C) HO: μ ≥ 10 vs. HA: μ < 10
D) HO: μ ≠10 vs. HA: μ = 10
E) HO: μ ≤ 10 vs. HA: μ > 10
Answer: E Difficulty: Medium
150. Calculate the appropriate test statistic to test the hypotheses.
A) 2.97
B) -2.97
C) 2.68
D) 1.34
E) -1.34
Answer: D Difficulty: Medium
151. Calculate the p-value for the test statistic.
A) 0.0901
B) 0.0037
C) 0.0015
D) -0.0015
E) -0.0901
Answer: A Difficulty: Medium
152. How much evidence do we have that the mean score exceeds 10?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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.
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257
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 ≠ 7.5
B) HO: μ ≥ 7.5 vs. HA: μ < 7.5
C) HO: μ ≥ 7.01 vs. HA: μ < 7.01
D) HO: μ ≠ 7.5 vs. HA: μ = 7.5
E) HO: μ ≤ 7.5 vs. HA: μ > 7.5
Answer: B Difficulty: Medium
154. Calculate the appropriate test statistic to test the hypotheses.
A) -13.10
B) -2.53
C) -1.31
D) 1.31
E) 2.53
Answer: C Difficulty: Medium
155. Calculate the p-value for the test statistic.
A) -0.0951
B) 0.0951
C) 0.1902
D) 0.0057
E) –0.0057
Answer: B Difficulty: Medium
156. How much evidence do we have that the mean years is less than 7.5?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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.
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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 ≠ 90,000
B) HO: μ ≥ 90,000 vs. HA: μ < 90,000
C) HO: μ ≥ 96,700 vs. HA: μ < 96,700
D) HO: μ ≠ 90,000 vs. HA: μ = 90,000
E) HO: μ ≤ 90,000 vs. HA: μ > 90,000
Answer: E Difficulty: Medium (AS)
158. Calculate the appropriate test statistic to test the hypotheses.
A) 2.47
B) 34.13
C) 478.16
D) -34.13
E) -2.47
Answer: A Difficulty: Medium (AS)
159. Calculate the p-value corresponding to the test statistic.
A) 0.0000
B) 0.0068
C) -0.0068
D) 0.0136
E) -0.0136
Answer: B Difficulty: Medium (AS)
160. How much evidence do we have that the major engine failure will occur after 90,000
miles?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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.
Bowerman, Essentials of Business Statistics, 2/e
259
161. Set up the null and alternative hypotheses that would be used to halt production
A) HO: μ = 3.0 vs. HA: μ ≠ 3.0
B) HO: μ ≥ 3.0 vs. HA: μ < 3.0
C) HO: μ ≥ 3.1 vs. HA: μ < 3.1
D) HO: μ ≠ 3.0 vs. HA: μ = 3.0
E) HO: μ ≤ 3.0 vs. HA: μ > 3.0
Answer: E Difficulty: Medium
162. Calculate the appropriate test statistic to test the hypotheses.
A) 1.00
B) -1.00
C) 2.80
D) 1.41
E) -1.41
Answer: D Difficulty: Medium
163. Calculate the p-value for the test statistic.
A) -0.0793
B) 0.0398
C) 0.1587
D) -0.1587
E) 0.0793
Answer: 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) Yes
B) No
Answer: 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.
260
Bowerman, Essentials of Business Statistics, 2/e
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 ≠ 5
B) HO: μ ≥ 5 vs. HA: μ < 5
C) HO: μ ≥ 4.13 vs. HA: μ < 4.13
D) HO: μ ≠ 5 vs. HA: μ = 5
E) HO: μ ≤ 5 vs. HA: μ > 5
Answer: B Difficulty: Medium
166. Calculate the appropriate test statistic to test the hypotheses.
A) -2.73
B) -3.78
C) -0.455
D) 3.78
E) 2.73
Answer: A Difficulty: Medium
167. Calculate the p-value for this test statistic.
A) 0.0032
B) 0.0001
C) 0.3264
D) 0.0064
E) -0.0032
Answer: A Difficulty: Medium
168. How much evidence do we have that the machine is in specification?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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.
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261
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 ≠ 123
B) HO: μ ≥ 123 vs. HA: μ < 123
C) HO: μ ≥ 113.03 vs. HA: μ < 113.03
D) HO: μ ≠ 123 vs. HA: μ = 123
E) HO: μ ≤ 123 vs. HA: μ > 123
Answer: B Difficulty: Medium
170. Calculate the appropriate test statistic to test the hypotheses.
A) -0.38
B) 2.43
C) 0.38
D) -15.34
E) -2.43
Answer: E Difficulty: Medium
171. Calculate the p-value for this test statistic.
A) 0.4925
B) -0.0075
C) 0.0075
D) 0.015
E) 0.352
Answer: C Difficulty: Medium
172. How much evidence do we have that the water usage is less than the AWWA estimate?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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.
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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 ≠ 120
B) H0 µ ≥ 120 Ha µ < 120
C) H0 µ ≤ 120 Ha µ > 120
D) H0 µ ≠ 120 Ha µ = 120
E) H0 µ ≥ 118 Ha µ < 118
Answer: A Difficulty: Medium
174. Calculate the test statistic to test these hypotheses.
A) -2.82
B) -6.32
C) 5.64
D) -5.64
E) 2.82
Answer: A Difficulty: Medium
175. Calculate the p-value.
A) .0024
B) -.0024
C) .0000
D) -.0048
E) .0048
Answer: E Difficulty: Medium
176. How much evidence do we have to reject the null hypothesis?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very Strong evidence
E) Extremely Strong evidence
Answer: D Difficulty: Easy
177. Calculate a confidence interval to test the hypotheses at α = .01
A) [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
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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 = 8
B) H0 µ ≤ 7.983 Ha µ > 7.983
C) H0 µ ≤ 8
Ha µ > 8
D) H0 µ ≥ 8
Ha µ < 8
E) H0 µ = 8
Ha µ ≠ 8
Answer: E Difficulty: Medium
179. Calculate the test statistic
A) -0.785
B) -1.57
C) -3.04
D) 1.57
E) 0.785
Answer: A Difficulty: Medium
180. Calculate the p-value
A) .216
B) .432
C) .0012
D) .0582
E) .1164
Answer: B Difficulty: Medium
181. How much evidence do we have that the filling line should be stopped?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very Strong evidence
E) Extremely Strong evidence
Answer: A Difficulty: Easy
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182. Calculate a confidence interval to test the hypotheses at α = .05
A) [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 > .995
B) H0 µ ≠ 1 Ha µ = 1
C) H0 µ ≥ 1 Ha µ < 1
D) H0 µ = 1 Ha µ ≠ 1
E) H0 µ ≤ 1
Ha µ > 1
Answer: D Difficulty: Medium
184. Calculate the test statistic
A) -2.83
B) -1.41
C) -2.00
D) 2.83
E) 1.41
Answer: B Difficulty: Medium
185. Calculate the p-value
A) .0793
B) .1586
C) .0023
D) .0046
E) .0456
Answer: B Difficulty: Medium
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186. How much evidence do we have that the manufacturer’s claim is false?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very Strong evidence
E) Extremely Strong evidence
Answer: 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 < 350
B) H0 µ ≠ 375 Ha µ = 375
C) H0 µ = 375 Ha µ ≠ 375
D) H0 µ ≥ 375 Ha µ < 375
E) H0 µ ≤ 375 Ha µ > 375
Answer: C Difficulty: Medium
189. Calculate the test statistic
A) -16.00
B) -4.00
C) -2.00
D) 2.00
E) 4.00
Answer: C Difficulty: Medium
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190. Calculate the p-value
A) 0.0001
B) 0.0002
C) 0.0228
D) 0.0456
E) -0.0228
Answer: D Difficulty: Medium
191. How much evidence do we have that the shipment is meeting the specified value?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very Strong evidence
E) Extremely Strong evidence
Answer: C Difficulty: Easy
192. Calculate a confidence interval to test the hypotheses at α = .01
A) [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 < 0.250
B) H 0 µ = 0.250 Ha µ ≠ 0.250
C) H 0 µ ≤ 0.250 Ha µ > 0.250
D) H 0 µ ≠ 0.250 Ha µ = 0.250
E) H 0 µ ≤ 0.2525 Ha µ > 0.2525
Answer: B Difficulty: Medium
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194. Calculate the test statistic
A) 7.187
B) .337
C) 3.371
D) -.337
E) -7.187
Answer: A Difficulty: Medium
195. What is the rejection point for α = .001 to test this hypothesis.
A) 2.575
B) 2.33
C) 3.09
D) 1.96
E) 3.29
Answer: E Difficulty: Medium
196. How much evidence do we have that the process is out of control
A) No evidence
B) Some evidence
C) Strong evidence
D) Very Strong evidence
E) Extremely Strong evidence
Answer: E Difficulty: Medium
197. Calculate a confidence interval to test the hypotheses at α = .01
A) [.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.
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198. Set up the null and alternative hypotheses to determine is the figure has changed.
A) H0 µ = 74914 Ha µ ≠ 74914
B) H 0 µ ≥ 74914 Ha µ < 74914
C) H 0 µ ≤ 74914 Ha µ > 74914
D) H 0 µ ≠ 74914 Ha µ = 74914
E) H 0 µ ≤ 81342 Ha µ > 81342
Answer: A Difficulty: Medium
199. Calculate the test statistic
A) 4.50
B) 47.61
C) 9.00
D) -47.61
E) -4.50
Answer: A Difficulty: Medium
200. What is the rejection point for testing these hypotheses at α = .05.
A) 1.28
B) 1.645
C) 1.96
D) 2.33
E) 2.575
Answer: C Difficulty: Medium
201. How much evidence do we have that the figure has changed?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very Strong evidence
E) Extremely Strong evidence
Answer: E Difficulty: Easy
202. Calculate a confidence interval to test the hypotheses at α = .001
A) [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
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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 > 60
B) H0 µ ≥ 60 Ha µ< 60
C) H0 µ = 55 Ha µ ≠ 55
D) H0 µ = 60 Ha µ ≠ 60
E) H0 µ ≠ 60 Ha µ = 60
Answer: D Difficulty: Medium
204. Calculate the test statistic
A) 5.92
B) 63.89
C) 11.84
D) -5.92
E) -63.89
Answer: D Difficulty: Medium
205. What is the rejection point for testing these hypotheses at α = .01.
A) 1.28
B) 1.645
C) 1.96
D) 2.33
E) 2.575
Answer: E Difficulty: Medium
206. How much evidence do we have that this company’s employees are different from the
average national employee?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very Strong evidence
E) Extremely Strong evidence
Answer: E Difficulty: Easy
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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 < 13
B) H0 µ = 13
Ha µ ≠ 13
C) H0 µ ≤ 13
Ha µ > 13
D) H0 µ ≠ 13
Ha µ = 13
E) H0 µ ≤ 12.58 Ha µ > 12.58
Answer: B Difficulty: Medium
209. Calculate the test statistic to test these hypotheses
A) 9.35
B) -9.35
C) 4.68
D) -4.68
E) -1.68
Answer: B Difficulty: Medium
210. What is the rejection point for testing these hypotheses at α = .001.
A) 1.28
B) 1.645
C) 2.575
D) 3.09
E) 3.291
Answer: E Difficulty: Medium
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211. How much evidence do we have that the mean of the process is not 13 ounces?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very Strong evidence
E) Extremely Strong evidence
Answer: E Difficulty: Easy
212. Calculate a confidence interval to test the hypotheses at α = .10
A) [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 ≤ 14.64
B) H0 µ ≤ 14.5
Ha µ > 14.5
C) H0 µ ≥ 14.5
Ha µ < 14.5
D) H0 µ = 14.5
Ha µ ≠ 14.5
E) H0 µ ≠ 14.5
Ha µ = 14.5
Answer: D Difficulty: Medium
214. Calculate the test statistic
A) 3.13
B) 1.98
C) 3.96
D) -3.13
E) -1.98
Answer: A Difficulty: Medium
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215. What is the rejection point for testing the hypotheses at α = .01.
A) 3.09
B) 3.29
C) 2.33
D) 2.575
E) 1.96
Answer: D Difficulty: Medium
216. How much evidence is there that the cans contain 14.5 ounces of cherries and juice?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very Strong evidence
E) Extremely Strong evidence
Answer: D Difficulty: Easy
217. Calculate a confidence interval to test the hypotheses at α = .05
A) [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 = 60
B) H0 µ ≥ 40 Ha µ < 40
C) H0 µ ≥ 60 Ha µ < 60
D) H0 µ ≤ 60 Ha µ > 60
E) H0 µ = 60 Ha µ ≠ 60
Answer: E Difficulty: Medium
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219. Calculate the test statistic
A) 2.91
B) -2.91
C) -3.57
D) 6.15
E) 3.57
Answer: A Difficulty: Medium
220. Calculate the p-value
A) 0.0000
B) 0.0018
C) 0.0036
D) 0.0009
E) 0.3859
Answer: D Difficulty: Easy
221. How much evidence do we have to reject the null hypothesis?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very Strong evidence
E) Extremely Strong evidence
Answer: D Difficulty: Easy
222. Calculate a confidence interval to test the hypotheses at α = .002
A) [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.
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223. Set up the null and alternative hypotheses to test the workers’ claim.
A) HO: μ = 50 vs. HA: μ ≠ 50
B) HO: μ ≥ 50 vs. HA: μ < 50
C) HO: μ ≥ 51.05 vs. HA: μ < 51.05
D) HO: μ ≠ 50 vs. HA: μ = 50
E) HO: μ ≤ 50 vs. HA: μ > 50
Answer: E Difficulty: Medium
224. Calculate the appropriate test statistic to test the hypotheses.
A) 2.38
B) 1.19
C) -1.19
D) 1.76
E) -1.76
Answer: B Difficulty: Medium
225. What is the rejection point for α = .05 to test the hypotheses.
A) 1.711
B) 2.064
C) 2.060
D) 1.708
E) 1.645
Answer: A Difficulty: Medium
226. How much evidence do we have that the workers’ claim is true?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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.
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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 ≠ 50
B) HO: μ ≥ 54 vs. HA: μ < 54
C) HO: μ ≥ 50 vs. HA: μ < 50
D) HO: μ ≠ 50 vs. HA: μ = 50
E) HO: μ ≤ 50 vs. HA: μ > 50
Answer: E Difficulty: Medium
228. Calculate the appropriate test statistic to test the hypotheses.
A) -2.00
B) -2.50
C) 12.50
D) 2.50
E) 2.00
Answer: D Difficulty: Medium
229. What is the rejection point for α = .01 to test the hypotheses.
A) 2.485
B) 2.797
C) 2.492
D) 2.787
E) 2.327
Answer: C Difficulty: Medium
230. How much evidence do we have that there is a slowdown?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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).
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231. Set up the null and alternative hypotheses to test whether the original research claim is
valid,
A) HO: μ = 15 vs. HA: μ ≠ 15
B) HO: μ ≥ 15 vs. HA: μ < 15
C) HO: μ ≥ 18.5 vs. HA: μ < 18.5
D) HO: μ ≠ 15 vs. HA: μ = 15
E) HO: μ ≤ 15 vs. HA: μ > 15
Answer: E Difficulty: Medium
232. Calculate the appropriate test statistic to test the hypotheses.
A) 3.39
B) 13.125
C) 0.875
D) -0.875
E) -3.39
Answer: A Difficulty: Medium
233. What is the rejection point for α = .001 to test the hypotheses.
A) 4.140
B) -4.140
C) 4.073
D) 3.291
E) 3.787
Answer: E Difficulty: Easy
234. How much evidence do we have that cell phone conversations are longer than the original
claim?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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.
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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 ≠ 400
B) HO: μ ≥ 400 vs. HA: μ < 400
C) HO: μ ≥ 550.4 vs. HA: μ < 550.4
D) HO: μ ≠ 400 vs. HA: μ = 400
E) HO: μ ≤ 400 vs. HA: μ > 400
Answer: E Difficulty: Medium
236. Calculate the appropriate test statistic to test the hypotheses.
A) 6.20
B) 1.72
C) 0.477
D) -6.20
E) -1.72
Answer: B Difficulty: Medium
237. What is the rejection point for α = .10 to test the hypotheses.
A) -1.356
B) 1.356
C) 1.282
D) 1.782
E) -1.782
Answer: B Difficulty: Medium
238. How much evidence do we have that the mean life is more than 400 hours?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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.
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239. Set up the null and alternative hypotheses to test whether the standard is being met
A) HO: μ = 15 vs. HA: μ ≠ 15
B) HO: μ ≥ 15 vs. HA: μ < 15
C) HO: μ ≥ 12.3 vs. HA: μ < 12.3
D) HO: μ ≠ 15 vs. HA: μ = 15
E) HO: μ ≤ 15 vs. HA: μ > 15
Answer: B Difficulty: Medium (AS)
240. Calculate the appropriate test statistic to test the hypotheses.
A) 7.50
B) 1.94
C) 3.88
D) -7.50
E) -1.94
Answer: E Difficulty: Medium (AS)
241. What is the rejection point for α = .05 to test the hypotheses.
A) -1.761
B) -1.753
C) -2.145
D) 1.645
E) 2.132
Answer: 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 evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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.
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243. Set up the null and alternative hypotheses to test the quality manager’s claim.
A) HO: μ = 20 vs. HA: μ ≠ 20
B) HO: μ ≥ 20 vs. HA: μ < 20
C) HO: μ ≥ 19.7 vs. HA: μ < 19.7
D) HO: μ ≠ 20 vs. HA: μ = 20
E) HO: μ ≤ 20 vs. HA: μ > 20
Answer: A Difficulty: Medium
244. Calculate the appropriate test statistic to test the hypotheses.
A) 3.00
B) 1.00
C) -9.00
D) -1.00
E) -3.00
Answer: E Difficulty: Medium
245. What is the rejection point for α = .05 to test the hypotheses.
A) 2.306
B) 2.262
C) 1.860
D) 3.09
E) 1.96
Answer: A Difficulty: Easy
246. How much evidence do we have to reject the null hypothesis?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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.
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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 ≠ 20
B) HO: μ ≥ 20 vs. HA: μ < 20
C) HO: μ ≥ 17.17 vs. HA: μ < 17.17
D) HO: μ ≠ 20 vs. HA: μ = 20
E) HO: μ ≤ 20 vs. HA: μ > 20
Answer: B Difficulty: Medium
248. Calculate the appropriate test statistic to test the hypotheses.
A) 3.00
B) 9.50
C) -0.95
D) -3.00
E) -9.50
Answer: D Difficulty: Medium
249. What is the rejection point for α = .01 to test the hypotheses.
A) -2.821
B) -3.250
C) -2.33
D) 2.821
E) 3.250
Answer: A Difficulty: Easy
250. How much evidence do we have that the new catalytic converter type meets the pollution
standard?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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.
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251. Set up the null and alternative hypotheses to test the claim.
A) HO: μ = 19 vs. HA: μ ≠ 19
B) HO: μ ≥ 19 vs. HA: μ < 19
C) HO: μ ≥ 20 vs. HA: μ < 20
D) HO: μ ≠ 19 vs. HA: μ = 19
E) HO: μ ≤ 19 vs. HA: μ > 19
Answer: A Difficulty: Medium
252. Calculate the appropriate test statistic to test the hypotheses.
A) 1.08
B) 0.54
C) -1.08
D) -0.54
E) 3.60
Answer: B Difficulty: Medium
253. What is the rejection point for α = .10 to test the hypotheses.
A) 1.729
B) 1.725
C) 1.328
D) 1.325
E) 1.645
Answer: A Difficulty: Easy
254. How much evidence do we have to reject the null hypothesis?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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.
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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 ≠ 471
B) HO: μ ≥ 471 vs. HA: μ < 471
C) HO: μ ≥ 174 vs. HA: μ < 174
D) HO: μ ≠ 471 vs. HA: μ = 471
E) HO: μ ≤ 471 vs. HA: μ > 471
Answer: E Difficulty: Medium (AS)
256. Calculate the appropriate test statistic to test the hypotheses.
A) 2.84
B) 13.61
C) 30.34
D) -2.84
E) -13.61
Answer: A Difficulty: Medium (AS)
257. What is the rejection point for α = .001 to test the hypotheses.
A) 3.792
B) 3.767
C) 3.505
D) 3.485
E) 3.09
Answer: C Difficulty: Medium (AS)
258. How much evidence do we have that the designer’s claim is true?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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.
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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 ≠ 15.5
B) HO: μ ≥ 15.5 vs. HA: μ < 15.5
C) HO: μ ≥ 15.42 vs. HA: μ < 15.42
D) HO: μ ≠ 15.5 vs. HA: μ = 15.5
E) HO: μ ≤ 15.5 vs. HA: μ > 15.5
Answer: A Difficulty: Medium
260. Calculate the appropriate test statistic to test the hypotheses.
A) -0.50
B) -2.06
C) -8.50
D) 0.50
E) 2.06
Answer: B Difficulty: Medium
261. What is the rejection point for α = .10 to test the hypotheses.
A) 1.746
B) 1.740
C) 1.337
D) 1.282
E) 1.645
Answer: A Difficulty: Easy
262. How much evidence do we have that the system differs from 15.5?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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.
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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 > .52
B) H0: ρ ≥ .50 vs HA: ρ < .50
C) H0: ρ ≤ .50 vs HA: ρ > .50
D) H0: ρ = .50 vs HA: ρ ≠ .50
E) H0: ρ ≠ .50 vs HA: ρ = .50
Answer: C Difficulty: Medium
264. Calculate the appropriate test statistic to test the hypotheses.
A) 0.80
B) 1.60
C) 8.00
D) -1.60
E) -0.80
Answer: A Difficulty: medium
265. Calculate the p-value associated with the test statistic.
A) .0001
B) .2000
C) .2119
D) .2881
E) .4238
Answer: 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 evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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.
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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 > .37
B) H0: ρ ≥ .33 vs HA: ρ < .33
C) H0: ρ ≤ .33 vs HA: ρ > .33
D) H0: ρ = .33 vs HA: ρ ≠ .33
E) H0: ρ ≠ .33 vs HA: ρ = .33
Answer: C Difficulty: Medium
268. Calculate the appropriate test statistic to test the hypotheses.
A) 1.853
B) 1.157
C) 1.902
D) 2.710
E) -1.902
Answer: C Difficulty: Medium
269. Calculate the p-value associated with the test statistic.
A) .0034
B) .0287
C) .0322
D) .0547
E) .1230
Answer: 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 evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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)
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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 > .44
B) H0: ρ ≥ .50 vs HA: ρ < .50
C) H0: ρ ≤ .50 vs HA: ρ > .50
D) H0: ρ = .50 vs HA: ρ ≠ .50
E) H0: ρ ≠ .50 vs HA: ρ = .50
Answer: B Difficulty: Medium
272. Calculate the appropriate test statistic to test the hypotheses.
A) 3.82
B) 3.79
C) 2.52
D) -2.54
E) -3.79
Answer: E Difficulty: Medium
273. Calculate the p-value associated with the test statistic.
A) -0.0001
B) 0.0001
C) 0.0055
D) 0.0059
E) 0.4990
Answer: 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 evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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.
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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 > .18
B) H0: ρ ≥ .20 vs HA: ρ < .20
C) H0: ρ ≤ .20 vs HA: ρ > .20
D) H0: ρ = .20 vs HA: ρ ≠ .20
E) H0: ρ ≠ .20 vs HA: ρ = .20
Answer: B Difficulty: Medium
276. Calculate the appropriate test statistic to test the hypotheses.
A) 5.00
B) 0.50
C) 0.212
D) -0.50
E) -1.00
Answer: D Difficulty: Medium
277. Calculate the p-value associated with the test statistic.
A) 0.1587
B) 0.3085
C) 0.4168
D) 0.0001
E) -0.3085
Answer: 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 evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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.
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279. Set up the appropriate hypotheses to test the advertising department’s claim.
A) H0: ρ ≤ .365 vs. HA: ρ > .365
B) H0: ρ ≥ .250 vs. HA: ρ < .250
C) H0: ρ ≤ .250 vs. HA: ρ > .250
D) H0: ρ = .250 vs. HA: ρ ≠ .250
E) H0: ρ ≠ .250 vs. HA: ρ = .250
Answer: C Difficulty: Medium (AS)
280. Calculate the appropriate test statistic to test the hypotheses.
A) -5.31
B) -4.69
C) 3.21
D) 4.69
E) 5.31
Answer: E Difficulty: Medium (AS)
281. Find the rejection point for testing these hypotheses at α = .001.
A) 3.09
B) 2.575
C) 2.33
D) 1.96
E) 3.00
Answer: 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 evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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.
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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 > .42
B) H0: ρ ≥ .50 vs HA: ρ < .50
C) H0: ρ ≤ .50 vs HA: ρ > .50
D) H0: ρ = .50 vs HA: ρ ≠ .50
E) H0: ρ ≠ .50 vs HA: ρ = .50
Answer: D Difficulty: Medium
284. Calculate the appropriate test statistic to test the hypotheses.
A) 2.99
B) 3.03
C) -2.99
D) -3.03
E) -1.94
Answer: C Difficulty: Medium
285. Calculate the p-value associated with the test statistic.
A) .0028
B) .0262
C) .0525
D) .0014
E) .0012
Answer: A Difficulty: Easy
286. How much evidence do we have that the region differs from the national population?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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
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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 > .780
B) H0: ρ ≥ .250 vs HA: ρ < .250
C) H0: ρ ≤ .250 vs HA: ρ > .250
D) H0: ρ = .250 vs HA: ρ ≠ .250
E) H0: ρ ≠ .250 vs HA: ρ = .250
Answer: D Difficulty: Medium
289. Calculate the appropriate test statistic to test the hypotheses.
A) -16.13
B) -15.43
C) 13.63
D) 15.43
E) 16.13
Answer: E Difficulty: Medium
290. Find the rejection point to test the hypotheses at α = .001.
A) 1.645
B) 1.960
C) 2.575
D) 3.090
E) 3.291
Answer: 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 evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: E Difficulty: Easy
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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 > .21
B) H0: ρ ≥ .17 vs HA: ρ < .17
C) H0: ρ ≤ .17 vs HA: ρ > .17
D) H0: ρ = .17 vs HA: ρ ≠ .17
E) H0: ρ ≠ .17 vs HA: ρ = .17
Answer: C Difficulty: Medium (AS)
294. Calculate the appropriate test statistic to test the hypotheses.
A) 2.25
B) 2.44
C) 1.11
D) -2.25
E) -2.44
Answer: B Difficulty: Medium (AS)
295. Calculate the p-value associated with the test statistic.
A) .0146
B) .0122
C) .0073
D) .1335
E) .0244
Answer: C Difficulty: Easy (AS)
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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 evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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 > .210
B) H0: ρ ≥ .250 vs. HA: ρ < .250
C) H0: ρ ≤ .250 vs. HA: ρ > .250
D) H0: ρ = .250 vs. HA: ρ ≠ .250
E) H0: ρ ≠ .250 vs. HA: ρ = .250
Answer: D Difficulty: Medium
298. Calculate the appropriate test statistic to test the hypotheses.
A) -2.15
B) -2.00
C) -0.91
D) 2.00
E) 2.51
Answer: B Difficulty: Medium
299. Calculate the p-value associated with the test statistic.
A) 0.0228
B) 0.0456
C) 0.1814
D) 0.3628
E) 0.4772
Answer: B Difficulty: Easy
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300. How much evidence do we have to reject the null hypothesis in favor of the alternative
hypothesis?
A) No evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: 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 > .39
B) H0: ρ ≥ .40 vs. HA: ρ < .40
C) H0: ρ ≤ .40 vs. HA: ρ > .40
D) H0: ρ = .40 vs. HA: ρ ≠ .40
E) H0: ρ ≠ .40 vs. HA: ρ = .40
Answer: B Difficulty: Medium
303. Calculate the appropriate test statistic to test the hypotheses.
A) 0.20
B) 0.40
C) -0.13
D) -0.20
E) -0.40
Answer: D Difficulty: Medium
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304. Calculate the p-value associated with the test statistic.
A) 0.0793
B) 0.1554
C) 0.3446
D) 0.4207
E) 0.4483
Answer: 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 evidence
B) Some evidence
C) Strong evidence
D) Very strong evidence
E) Extremely strong evidence
Answer: A Difficulty: Easy
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