CHAPTER 9—HYPOTHESIS TESTS
MULTIPLE CHOICE
1. More evidence against H0 is indicated by
a.
lower levels of significance
b.
smaller p-values
c.
smaller critical values
d.
lower probabilities of a Type II error
2. Two approaches to drawing a conclusion in a hypothesis test are
a.
p-value and critical value
b.
one-tailed and two-tailed
c.
Type I and Type II
d.
null and alternative
3. As a general guideline, the research hypothesis should be stated as the
a.
null hypothesis
b.
alternative hypothesis
c.
tentative assumption
d.
hypothesis the researcher wants to disprove
4. A Type I error is committed when
a.
a true alternative hypothesis is not accepted
b.
a true null hypothesis is rejected
c.
the critical value is greater than the value of the test statistic
d.
sample data contradict the null hypothesis
5. Which of the following hypotheses applies to a situation where action must be taken both when H0
cannot be rejected and when H0 can be rejected?
a.
b.
c.
d.
6. The practice of concluding “do not reject H0” is preferred over “accept H0” when we
a.
are conducting a one-tailed test
b.
are testing the validity of a claim
c.
have an insufficient sample size
d.
have not controlled for the Type II error
7. If the cost of a Type I error is high, a smaller value should be chosen for the
a.
critical value
b.
confidence coefficient
c.
level of significance
d.
test statistic
8. When the rejection region is in the lower tail of the sampling distribution, the p-value is the area under
the curve
a.
less than or equal to the critical value
b.
less than or equal to the test statistic
c.
greater than or equal to the critical value
d.
greater than or equal to the test statistic
9. In tests about a population proportion, p0 represents the
a.
hypothesized population proportion
b.
observed sample proportion
c.
observed p-value
d.
probability of
10. Which of the following is an improper form of the null and alternative hypotheses?
a.
and
b.
and
c.
and
d.
and
11. For a two-tailed hypothesis test about
, we can use any of the following approaches except
a.
compare the confidence interval estimate of
to the hypothesized value of
b.
compare the p-value to the value of
c.
compare the value of the test statistic to the critical value
d.
compare the level of significance to the confidence coefficient
12. An example of statistical inference is
a.
a population mean
b.
descriptive statistics
c.
calculating the size of a sample
d.
hypothesis testing
13. In hypothesis testing, the hypothesis tentatively assumed to be true is
a.
the alternative hypothesis
b.
the null hypothesis
c.
either the null or the alternative
d.
None of the other answers are correct.
14. In hypothesis testing, the alternative hypothesis is
a.
the hypothesis tentatively assumed true in the hypothesis-testing procedure
b.
the hypothesis concluded to be true if the null hypothesis is rejected
c.
the maximum probability of a Type I error
d.
All of the answers are correct.
15. Your investment executive claims that the average yearly rate of return on the stocks she recommends
is at least 10.0%. You plan on taking a sample to test her claim. The correct set of hypotheses is
a.
H0:
10.0% Ha:
10.0%
b.
H0:
10.0% Ha:
10.0%
c.
H0:
10.0% Ha:
10.0%
d.
H0:
10.0% Ha:
10.0%
16. A meteorologist stated that the average temperature during July in Chattanooga was 80 degrees. A
sample of 32 Julys was taken. The correct set of hypotheses is
a.
H0:
80 Ha:
80
b.
H0:
80 Ha:
> 80
c.
H0:
80 Ha:
= 80
d.
None of the other answers are correct.
17. A student believes that the average grade on the final examination in statistics is at least 85. She plans
on taking a sample to test her belief. The correct set of hypotheses is
a.
H0:
85 Ha:
85
b.
H0:
85 Ha:
85
c.
H0:
85 Ha:
85
d.
None of the other answers are correct.
18. The average life expectancy of tires produced by the Whitney Tire Company has been 40,000 miles.
Management believes that due to a new production process, the life expectancy of its tires has
increased. In order to test the validity of this belief, the correct set of hypotheses is
a.
H0:
40,000 Ha:
40,000
b.
H0:
40,000 Ha:
40,000
c.
H0:
40,000 Ha:
40,000
d.
H0:
40,000 Ha:
40,000
19. A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink.
Any overfilling or underfilling results in the shutdown and readjustment of the machine. To determine
whether or not the machine is properly adjusted, the correct set of hypotheses is
a.
H0:
< 12 Ha:
12
b.
H0:
12 Ha:
12
c.
H0:
12 Ha:
= 12
d.
H0:
= 12 Ha:
12
20. The manager of an automobile dealership is considering a new bonus plan in order to increase sales.
Currently, the mean sales rate per salesperson is five automobiles per month. The correct set of
hypotheses for testing the effect of the bonus plan is
a.
H0:
5 Ha:
5
b.
H0:
5 Ha:
5
c.
H0:
5 Ha:
5
d.
H0:
5 Ha:
5
21. In hypothesis testing if the null hypothesis is rejected,
a.
no conclusions can be drawn from the test
b.
the alternative hypothesis must also be rejected
c.
the data must have been accumulated incorrectly
d.
None of the other answers are correct.
22. If a hypothesis test leads to the rejection of the null hypothesis, a
a.
Type II error must have been committed
b.
Type II error may have been committed
c.
Type I error must have been committed
d.
Type I error may have been committed
23. The error of rejecting a true null hypothesis is
a.
a Type I error
b.
a Type II error
c.
can be either a or b, depending on the situation
d.
committed when not enough information is available
24. In hypothesis testing if the null hypothesis has been rejected when the alternative hypothesis has been
true,
a.
a Type I error has been committed
b.
a Type II error has been committed
c.
either a Type I or Type II error has been committed
d.
the correct decision has been made
25. A Type II error is committed when
a.
a true alternative hypothesis is mistakenly rejected
b.
a true null hypothesis is mistakenly rejected
c.
the sample size has been too small
d.
not enough information has been available
26. The probability of making a Type I error is denoted by
a.
b.
c.
1 −
d.
1 −
27. The level of significance is the
a.
maximum allowable probability of Type II error
b.
maximum allowable probability of Type I error
c.
same as the confidence coefficient
d.
same as the p-value
28. The level of significance in hypothesis testing is the probability of
a.
accepting a true null hypothesis
b.
accepting a false null hypothesis
c.
rejecting a true null hypothesis
d.
could be any of the above, depending on the situation
29. In the hypothesis testing procedure, is
a.
the level of significance
b.
the critical value
c.
the confidence level
d.
1 − level of significance
30. The level of significance can be any
a.
negative value
b.
value
c.
value larger than 0.1
d.
None of the answers is correct.
31. In hypothesis testing, the critical value is
a.
a number that establishes the boundary of the rejection region
b.
the probability of a Type I error
c.
the probability of a Type II error
d.
the same as the p–value
32. A one-tailed test is a
a.
hypothesis test in which rejection region is in both tails of the sampling distribution
b.
hypothesis test in which rejection region is in one tail of the sampling distribution
c.
hypothesis test in which rejection region is only in the lower tail of the sampling
distribution
d.
hypothesis test in which rejection region is only in the upper tail of the sampling
distribution
33. A two-tailed test is a
a.
hypothesis test in which rejection region is in both tails of the sampling distribution
b.
hypothesis test in which rejection region is in one tail of the sampling distribution
c.
hypothesis test in which rejection region is only in the lower tail of the sampling
distribution
d.
hypothesis test in which rejection region is only in the upper tail of the sampling
distribution
34. Read the z statistics from the normal distribution table and circle the correct answer. A two-tailed test
at a .0694 level of significance; z =
a.
-1.96 and 1.96
b.
-1.48 and 1.48
c.
-1.09 and 1.09
d.
-0.86 and 0.86
35. Read the z statistic from the normal distribution table and circle the correct answer. A one-tailed test
(lower tail) at a .063 level of significance; z =
a.
-1.86
b.
-1.53
c.
-1.96
d.
-1.645
36. Read the z statistic from the normal distribution table and circle the correct answer. A one-tailed test
(upper tail) at a .123 level of significance; z =
a.
1.54
b.
1.96
c.
1.645
d.
1.16
37. When the hypotheses H0:
100 and Ha:
100 are being tested at a level of significance of , the
null hypothesis will be rejected if the test statistic z is
a.
> z
b.
> –z
c.
< –z
d.
< 100
38. In order to test the hypotheses H0: 100 and Ha:
100 at an level of significance, the null
hypothesis will be rejected if the test statistic z is
a.
z
b.
z
c.
–z
d.
100
39. For a one-tailed test (upper tail) with a sample size of 900, the null hypothesis will be rejected at the
.05 level of significance if the test statistic is
a.
less than or equal to -1.645
b.
greater than or equal to 1.645
c.
less than 1.645
d.
less than -1.96
40. For a two-tailed test with a sample size of 40, the null hypothesis will not be rejected at a 5% level of
significance if the test statistic is
a.
between -1.96 and 1.96, exclusively
b.
greater than 1.96
c.
less than 1.645
d.
greater than -1.645
41. If a hypothesis is rejected at a 5% level of significance, it
a.
will always be rejected at the 1% level
b.
will always be accepted at the 1% level
c.
will never be tested at the 1% level
d.
may be rejected or not rejected at the 1% level
42. If a hypothesis is not rejected at a 5% level of significance, it will
a.
also not be rejected at the 1% level
b.
always be rejected at the 1% level
c.
sometimes be rejected at the 1% level
d.
Not enough information is given to answer this question.
43. A p–value is the
a.
probability, when the null hypothesis is true, of obtaining a sample result that is at least as
unlikely as what is observed
b.
value of the test statistic
c.
probability of a Type II error
d.
probability corresponding to the critical value(s) in a hypothesis test
44. Which of the following does not need to be known in order to compute the p-value?
a.
knowledge of whether the test is one-tailed or two-tailed
b.
the value of the test statistic
c.
the level of significance
d.
All of these are needed.
45. When the p-value is used for hypothesis testing, the null hypothesis is rejected if
a.
p-value
b.
p-value
c.
p-value
d.
p-value = z
46. A two-tailed test is performed at a 5% level of significance. The p-value is determined to be 0.09. The
null hypothesis
a.
must be rejected
b.
should not be rejected
c.
may or may not be rejected, depending on the sample size
d.
has been designed incorrectly
47. Excel’s __________ function can be used to calculate a p-value for a hypothesis test.
a.
RAND
b.
NORM.S.DIST
c.
NORM.S.INV
d.
Not enough information is given to answer this question.
48. When using Excel to calculate a p-value for an upper-tail hypothesis test, the following must be used
a.
RAND
b.
1 − NORM.S.DIST
c.
NORM.S.DIST
d.
Not enough information is given to answer this question.
49. When using Excel to calculate a p-value for a lower-tail hypothesis test, the following must be used
a.
RAND
b.
1 − NORM.S.DIST
c.
NORM.S.DIST
d.
Not enough information is given to answer this question.
50. For a sample size of 30, changing from using the standard normal distribution to using the t
distribution in a hypothesis test,
a.
will result in the rejection region being smaller
b.
will result in the rejection region being larger
c.
would have no effect on the rejection region
d.
Not enough information is given to answer this question.
51. Read the t statistic from the table of t distributions and circle the correct answer. A two-tailed test, a
sample of 20 at a .20 level of significance; t =
a.
1.328
b.
2.539
c.
1.325
d.
2.528
52. Read the t statistic from the table of t distributions and circle the correct answer. A one-tailed test
(upper tail), a sample size of 18 at a .05 level of significance t =
a.
2.12
b.
1.734
c.
-1.740
d.
1.740
53. Read the t statistic from the table of t distributions and circle the correct answer. A one-tailed test
(lower tail), a sample size of 10 at a .10 level of significance; t =
a.
1.383
b.
-1.372
c.
-1.383
d.
-2.821
54. Excel’s __________ function can be used to calculate a p-value for a hypothesis test when is
unknown.
a.
RAND
b.
T.DIST
c.
NORM.S.DIST
d.
Not enough information is given to answer this question.
55. The school’s newspaper reported that the proportion of students majoring in business is at least 30%.
You plan on taking a sample to test the newspaper’s claim. The correct set of hypotheses is
a.
H0: p < 0.30 Ha: p 0.30
b.
H0: p 0.30 Ha: p > 0.30
c.
H0: p 0.30 Ha: p < 0.30
d.
H0: p > 0.30 Ha: p 0.30
56. In the past, 75% of the tourists who visited Chattanooga went to see Rock City. The management of
Rock City recently undertook an extensive promotional campaign. They are interested in determining
whether the promotional campaign actually increased the proportion of tourists visiting Rock City. The
correct set of hypotheses is
a.
H0: p > 0.75 Ha: p 0.75
b.
H0: p < 0.75 Ha: p 0.75
c.
H0: p 0.75 Ha: p < 0.75
d.
H0: p 0.75 Ha: p > 0.75
57. The academic planner of a university thinks that at least 35% of the entire student body attends
summer school. The correct set of hypotheses to test his belief is
a.
H0: p > 0.35 Ha: p 0.35
b.
H0: p 0.35 Ha: p > 0.35
c.
H0: p 0.35 Ha: p < 0.35
d.
H0: p > 0.35 Ha: p 0.35
58. Which Excel function would not be appropriate to use when conducting a hypothesis test for a
population proportion?
a.
NORM.S.DIST
b.
COUNTIF
c.
STDEV
d.
All are appropriate.
Exhibit 9-1
H0:
20
Ha:
20
59. Refer to Exhibit 9-1. The test statistic equals
a.
2.3
b.
0.38
c.
-2.3
d.
-0.38
60. Refer to Exhibit 9-1. The p-value is
a.
0.5107
b.
0.0214
c.
0.0107
d.
2.1
61. Refer to Exhibit 9-1. If the test is done at a .05 level of significance, the null hypothesis should
a.
not be rejected
b.
be rejected
c.
Not enough information is given to answer this question.
d.
None of the other answers are correct.
Exhibit 9-2
The manager of a grocery store has taken a random sample of 100 customers. The average length of
time it took the customers in the sample to check out was 3.1 minutes. The population standard
deviation is known to be 0.5 minutes. We want to test to determine whether or not the mean waiting
time of all customers is significantly more than 3 minutes.
62. Refer to Exhibit 9-2. The test statistic is
a.
1.96
b.
1.64
c.
2.00
d.
0.056
63. Refer to Exhibit 9-2. The p-value is
a.
0.025
b.
0.0456
c.
0.05
d.
0.0228
64. Refer to Exhibit 9-2. At a .05 level of significance, it can be concluded that the mean of the population
is
a.
significantly greater than 3
b.
not significantly greater than 3
c.
significantly less than 3
d.
significantly greater then 3.18
Exhibit 9-3
H0: = 50
Ha: 50
65. Refer to Exhibit 9-3. The test statistic equals
a.
0.1714
b.
0.3849
c.
-1.2
d.
1.2
66. Refer to Exhibit 9-3. The p-value is equal to
a.
0.1151
b.
0.3849
c.
0.2698
d.
0.2302
67. Refer to Exhibit 9-3. If the test is done at a 5% level of significance, the null hypothesis should
a.
not be rejected
b.
be rejected
c.
Not enough information given to answer this question.
d.
None of the other answers are correct.
Exhibit 9-4
A random sample of 16 students selected from the student body of a large university had an average
age of 25 years. We want to determine if the average age of all the students at the university is
significantly different from 24. Assume the distribution of the population of ages is normal with a
standard deviation of 2 years.
68. Refer to Exhibit 9-4. The test statistic is
a.
1.96
b.
2.00
c.
1.645
d.
0.05
69. Refer to Exhibit 9-4. At a .05 level of significance, it can be concluded that the mean age is
a.
not significantly different from 24
b.
significantly different from 24
c.
significantly less than 24
d.
significantly less than 25
Exhibit 9-5
H0:
80
Ha:
80
Assume population is normally distributed.
70. Refer to Exhibit 9-5. The test statistic equals
a.
-2.131
b.
-0.53
c.
0.53
d.
2.131
71. Refer to Exhibit 9-5. The p-value is equal to
a.
-0.0166
b.
0.0166
c.
0.0332
d.
0.9834
72. Refer to Exhibit 9-5. If the test is done at a 2% level of significance, the null hypothesis should
a.
not be rejected
b.
be rejected
c.
Not enough information is given to answer this question.
d.
None of the other answers are correct.
Exhibit 9-6
A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A.
We are interested in determining whether or not the proportion of the population in favor of Candidate
A is significantly more than 75%.
73. Refer to Exhibit 9-6. The test statistic is
a.
0.80
b.
0.05
c.
1.25
d.
2.00
74. Refer to Exhibit 9-6. The p-value is
a.
0.2112
b.
0.05
c.
0.025
d.
0.0156
75. Refer to Exhibit 9-6. At a .05 level of significance, it can be concluded that the proportion of the
population in favor of candidate A is
a.
significantly greater than 75%
b.
not significantly greater than 75%
c.
significantly greater than 80%
d.
not significantly greater than 80%
76. For a two-tailed hypothesis test about a population mean, the null hypothesis can be rejected if the
confidence interval
a.
is symmetric
b.
is non-symmetric
c.
includes
0
d.
does not include
0
77. In a two-tailed hypothesis test, the null hypothesis should be rejected if the p-value is
a.
less than or equal to
b.
less than or equal to 2
c.
greater than or equal to
d.
greater than or equal to 2
78. If a hypothesis test has a Type I error probability of .05, that means
a.
if the null hypothesis is false, it will not be rejected 5% of the time
b.
if the null hypothesis is false, it will be rejected 5% of the time
c.
if the null hypothesis is true, it will not be rejected 5% of the time
d.
if the null hypothesis is true, it will be rejected 5% of the time
79. For a two-tailed hypothesis test with a test statistic value of z = 2.05, the p–value is
a.
.0101
b.
.0202
c.
.0404
d.
.4899
80. The rejection region for a one-tailed hypothesis test
a.
has an area of 1 –
b.
has an area equal to the confidence coefficient
c.
is in the tail that supports the null hypothesis
d.
is in the tail that supports the alternative hypothesis
81. The smaller the p-value,
a.
the greater the evidence against H0
b.
the greater the chance of committing a Type II error
c.
the greater the chance of committing a Type I error
d.
the less likely you are to reject H0
PROBLEM
1. A researcher is testing a new painkiller that claims to relieve pain in less than 15 minutes, on average.
a.
State the hypotheses associated with the researcher’s test.
b.
Describe a Type I error for this situation.
c.
Describe a Type II error for this situation.
b.
A Type I error for this situation would be to incorrectly conclude that the average pain relief