chap10-TIF-BSAFC5
300 Two-Sample Tests and One-Way ANOVA
CHAPTER 10: TWO-SAMPLE TESTS AND ONE-WAY
ANOAVA
1.The t test for the difference between the means of 2 independent populations assumes that the
respective
a)sample sizes are equal.
b)sample variances are equal.
c)populations are approximately normal.
d)All of the above.
ANSWER:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: pooled variance, t test, assumption
2.The t test for the mean difference between 2 related populations assumes that the
a)population sizes are equal.
b)sample variances are equal.
c)population of differences is approximately normal or sample sizes are large enough.
d)All of the above.
ANSWER:
c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: t test, mean difference, assumption
3.If we are testing for the difference between the means of 2 related populations with samples of n1
= 20 and n2 = 20, the number of degrees of freedom is equal to
a)39.
b)38.
c)19.
d)18.
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: t test, mean difference, degrees of freedom
4.If we are testing for the difference between the means of 2 independent populations presuming
equal variances with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to
a)39.
b)38.
c)19.
d)18.
Two-Sample Tests and One-Way ANOVA 301 ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: pooled variance, t test, degrees of freedom
5.In what type of test is the variable of interest the difference between the values of the
observations rather than the observations themselves?
a) A test for the equality of variances from 2 independent populations.
b) A test for the difference between the means of 2 related populations.
c) A test for the difference between the means of 2 independent populations.
d)All of the above.
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: t test, mean difference
6.In testing for the differences between the means of 2 independent populations where the
variances in each population are unknown but assumed equal, the degrees of freedom are
a)n– 1.
b)n1 + n2– 1.
c)n1 + n2– 2.
d)n– 2.
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: pooled variance, t test, degrees of freedom
7.In testing for differences between the means of 2 related populations where the variance of the
differences is unknown, the degrees of freedom are
a)n– 1.
b)n1 + n2– 1.
c)n1 + n2– 2.
d)n– 2.
ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: t test, mean difference, degrees of freedom
8.In testing for differences between the means of two related populations, the null hypothesis is
a)
0: 2
D
Hμ=.
b)
0: 0
D
Hμ=.
c)
0: 0
D
Hμ<.
d)
0: 0
D
Hμ>. ANSWER:
b
TYPE: MC DIFFICULTY: Easy
302 Two-Sample Tests and One-Way ANOVA
KEYWORDS: t test, mean difference, form of hypothesis
9. In testing for differences between the means of two independent populations, the null hypothesis
is:
a) 012: H μμ- = 2. b) H 0: μ1–μ2 = 0. c) H 0: μ1–μ2 > 0. d) H 0: μ1–μ2 < 2.
ANSWER: b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: pooled variance, t test, form of hypothesis
10. When testing for the difference between 2 population variances with sample sizes of n 1 = 8 and
n 2 = 10, the number of degrees of freedom are
a) 8 and 10. b) 7 and 9. c) 18. d) 16.
ANSWER: b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: F test, difference between two variances, degrees of freedom
11. The statistical distribution used for testing the difference between two population variances is the
___ distribution.
a) t
b) standardized normal c) binomial d) F
ANSWER: d
TYPE: MC DIFFICULTY: Easy
KEYWORDS: F test, difference between two variances, degrees of freedom
12. The test for the equality of two population variances is based on
a) the difference between the 2 sample variances. b) the ratio of the 2 sample variances.
c) the difference between the 2 population variances.
d) the difference between the sample variances divided by the difference between the
sample means.
ANSWER: b
TYPE: MC DIFFICULTY: Easy
Two-Sample Tests and One-Way ANOVA 303 KEYWORDS: F test, difference between two variances
13. True or False: The F test used for testing the difference in two population variances is always a
one-tailed test.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: F test, difference between two variances, rejection region
14.In testing for the differences between the means of two related populations, the _______
hypothesis is the hypothesis of "no differences."
ANSWER:
null
TYPE: FI DIFFICULTY: Easy
KEYWORDS: t test, mean difference, form of hypothesis
15.In testing for the differences between the means of two related populations, we assume that the
differences follow a _______ distribution.
ANSWER:
normal
TYPE: FI DIFFICULTY: Easy
KEYWORDS: t test, mean difference, assumption
16.In testing for the differences between the means of two independent populations, we assume that
the 2 populations each follow a _______ distribution.
ANSWER:
normal
TYPE: FI DIFFICULTY: Easy
KEYWORDS: pooled variance, t test, assumption
17. Given the following information, calculate the degrees of freedom that should be used in the
pooled-variance t test.
s12 = 4 s22 = 6
n1 = 16 n2 = 25
a)df = 41
b)df = 39
c)df = 16
d)df = 25
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: pooled variance, t test, degrees of freedom
304 Two-Sample Tests and One-Way ANOVA
18.Given the following information, calculate s p2, the pooled sample variance that should be used in
the pooled-variance t test.
s12 = 4 s22 = 6
n1 = 16 n2 = 25
a)s p2 = 6.00
b)s p2 = 5.00
c)s p2 = 5.23
d)s p2 = 4.00
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: pooled variance, t test
TABLE 10-1
Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.
American Japanese
Sample Size 211 100
Mean SSATL Score 65.75 79.83
Population Std. Dev. 11.07 6.41
19.Referring to Table 10-1, judging from the way the data were collected, which test would likely
be most appropriate to employ?
a)Paired t test
b)Pooled-variance t test for the difference between two means
c)Independent samples Z test for the difference between two means
d)Related samples Z test for the mean difference
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: Z test, difference between two means
20.Referring to Table 10-1, give the null and alternative hypotheses to determine if the average
SSATL score of Japanese managers differs from the average SSATL score of American
managers.
a)H
0: μ
A
–μ
J
≥0 versus H
1
: μ
A
–μ
J
<0
b)H
0:μ
A
–μ
J
≤0versus H
1
: μ
A
–μ
J
>0
c)H
0: μ
A
–μ
J
=0versus H
1
:μ
A
–μ
J
≠0
d)H
0: X
A
–X
J
=0 versus H
1
:X
A
–X
J
≠0
ANSWER:
Two-Sample Tests and One-Way ANOVA 305
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: Z test, mean differences, form of hypothesis
21. Referring to Table 10-1, assuming the independent samples procedure was used, calculate the
value of the test statistic.
a) Z =
65.75–79.83
9.82211+9.82
100
b) Z =65.75–79.83
11.07211+6.41
100
c) Z =65.75–79.83
9.822211+9.82
2
100 d) Z =65.75–79.83
11.072211+6.41
2
100
ANSWER:
d
TYPE: MC DIFFICULTY: Easy
KEYWORDS: Z test, mean differences, test statistic
22. Referring to Table 10-1, suppose that the test statistic is Z = 2.45. Find the p -value if we assume
that the alternative hypothesis was a two-tailed test (0– :1≠J A H μμ).
a) 0.0071 b) 0.0142 c) 0.4929 d) 0.9858
ANSWER: b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: Z test, mean differences, p -value
306 Two-Sample Tests and One-Way ANOVA
TABLE 10-2
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.
23. Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA
graduates have a significantly lower mean starting salary than the male MBA graduates. According to the test run, which of the following is an appropriate alternative hypothesis?
a) 1females males :H μμ>
b) 1females males :H μμ< c) 1females males :H μμ≠ d) 1females males :H μμ=
ANSWER: b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: pooled variance, t test, form of hypothesis
24. Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA
graduates have a significantly lower mean starting salary than the male MBA graduates. From the analysis in Table 10-2, the correct test statistic is:
a) 0.0860 b) – 1.4019 c) – 1.7011 d) – 6,733.33
ANSWER:
Two-Sample Tests and One-Way ANOVA 307 b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: pooled variance, t test, test statistic
25.Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA
graduates have a significantly lower mean starting salary than the male MBA graduates. The proper conclusion for this test is:
a)At the α = 0.10 level, there is sufficient evidence to indicate a difference in the mean
starting salaries of male and female MBA graduates.
b)At the α = 0.10 level, there is sufficient evidence to indicate that females have a lower
mean starting salary than male MBA graduates.
c)At the α = 0.10 level, there is sufficient evidence to indicate that females have a higher
mean starting salary than male MBA graduates.
d)At the α = 0.10 level, there is insufficient evidence to indicate any difference in the
mean starting salaries of male and female MBA graduates.
ANSWER:
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: pooled variance, t test, conclusion
26.Referring to Table 10-2, the researcher was attempting to show statistically that the female MBA
graduates have a significantly lower mean starting salary than the male MBA graduates. What assumptions were necessary to conduct this hypothesis test?
a)Both populations of salaries (male and female) must have approximate normal
distributions.
b)The population variances are approximately equal.
c)The samples were randomly and independently selected.
d)All of the above assumptions were necessary.
ANSWER:
d
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: pooled variance, t test, assumption
27.Referring to Table 10-2, what is the 99% confidence interval estimate for the difference between
two means?
ANSWER:
-$20,004.90 to $6,538.30
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: confidence interval, difference between two means
28.Referring to Table 10-2, what is the 95% confidence interval estimate for the difference between
two means?
ANSWER:
-$16571.55 to $3,104.95
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: confidence interval, difference between two means
308 Two-Sample Tests and One-Way ANOVA
29. Referring to Table 10-2, what is the 90% confidence interval estimate for the difference between
two means?
ANSWER:
-$14,903.61 to $1,437.01
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: confidence interval, difference between two means
TABLE 10-3
The use of preservatives by food processors has become a controversial issue. Suppose 2
preservatives are extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative I and 15 are treated with preservative II, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarized in the table below.
Preservative I Preservative II
X I = 106.4 hours X II = 96.54 hours S I = 10.3 hours S II = 13.4 hours
30. Referring to Table 10-3, state the null and alternative hypotheses for testing if the population
variances differ for preservatives I and II.
a) 0– : versus 0– :221220<≥II I II
I H H σσσσ b) 0– : versus 0– :221220>≤II I II
I H H σσσσ c) 0– : versus 0– :221220≠=II I II
I H H σσσσ d) 0– : versus 0– :221220=≠II I II
I H H σσσσ ANSWER: c
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: F test, difference between two variances, form of hypothesis
31. Referring to Table 10-3, what is the value of the test statistic for testing if the population
variances differ for preservatives I and II?
ANSWER: 1.6925
TYPE: PR DIFFICULTY: Easy
KEYWORDS: F test, difference between two variances, test statistic
Two-Sample Tests and One-Way ANOVA 309 32.Referring to Table 10-3, what assumptions are necessary for testing if the population variances
differ for preservatives I and II?
a)Both sampled populations are normally distributed.
b)Both samples are random and independent.
c)Neither (a) nor (b) is necessary.
d)Both (a) and (b) are necessary.
ANSWER:
d
TYPE: MC DIFFICULTY: Easy
KEYWORDS: F test, difference between two variances, assumption
33.Referring to Table 10-3, what is the critical value for testing if the population variances differ for
preservatives I and II at the 5% level of significance?
ANSWER:
2.9786 (using Excel) or 2.95 (using Table E.5 with 15 and 14 degrees of freedom)
TYPE: PR DIFFICULTY: Easy
KEYWORDS: F test, difference between two variances, critical value
34.Referring to Table 10-3, what is the largest level of significance at which a test if the population
variances differ for preservatives I and II will not be rejected?
ANSWER:
0.3362 or …greater than 0.05? (using Table E.5 with 15 and 14 degrees of freedom)
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: F test, difference between two variances, p-value
35.Referring to Table 10-3, suppose = 0.05. Which of the following represents the result of the
relevant hypothesis test?
a)The alternative hypothesis is rejected.
b)The null hypothesis is rejected.
c)The null hypothesis is not rejected.
d)Insufficient information exists on which to make a decision.
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: F test, difference between two variances, decision
310 Two-Sample Tests and One-Way ANOVA
36.Referring to Table 10-3, suppose α = 0.05. Which of the following represents the correct
conclusion?
a)There is no evidence of a difference in the population variances betweeen preservatives I
and II.
b)There is evidence of a difference in the population variances betweeen preservatives I
and II.
c)There is no evidence that the population variances betweeen preservatives I and II are the
same.
d)There is evidence that the population variances betweeen preservatives I and II are the
same.
ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: F test, difference between two variances, conclusion
TABLE 10-4
A real estate company is interested in testing whether, on average, families in Gotham have been
living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random
sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: X G = 35 months, s G2 = 900 Metropolis: X M = 50 months, s M2 = 1050
37.Referring to Table 10-4, which of the following represents the relevant hypotheses tested by the
real estate company?
a)H
0: μ
G
–μ
M
≥0 versus H
1
:μ
G
–μ
M
<0
b)H
0:μ
G
–μ
M
≤0versus H
1
:μ
G
–μ
M
>0
c)H
0: μ
G
–μ
M
=0versus H
1
: μ
G
–μ
M
≠0
d)H
0: X
G
–X
M
≥0 versus H
1
: X
G
–X
M
<0
ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: pooled variance, t test, form of hypothesis
38.Referring to Table 10-4, what is the estimated standard error of the difference between the 2
sample means?
a) 4.06
b) 5.61
c)8.01
d)16.00
ANSWER:
Two-Sample Tests and One-Way ANOVA 311 a
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: pooled variance, t test, standard error
39.Referring to Table 10-4, what is an unbiased point estimate for the mean of the sampling
distribution of the difference between the 2 sample means?
a)– 22
b)– 10
c)– 15
d)0
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: pooled variance, t test, unbiased, point estimate
40.Referring to Table 10-4, what is(are) the critical value(s) of the relevant hypothesis test if the
level of significance is 0.05?
a)t?Z = – 1.645
b)t?Z = ±1.96
c)t?Z = – 1.96
d)t?Z = – 2.080
ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: pooled variance, t test, critical value
41.Referring to Table 10-4, what is(are) the critical value(s) of the relevant hypothesis test if the
level of significance is 0.01?
a)t?Z = – 1.96
b)t?Z = ±1.96
c)t?Z = – 2.080
d)t?Z = – 2.33
ANSWER:
d
TYPE: MC DIFFICULTY: Easy
KEYWORDS: pooled variance, t test, critical value
42.Referring to Table 10-4, what is the standardized value of the estimate of the mean of the
sampling distribution of the difference between sample means?
a)– 8.75
b)– 3.69
c)– 2.33
d)– 1.96
ANSWER:
312 Two-Sample Tests and One-Way ANOVA
b
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: pooled variance, t test, test statistic
43.Referring to Table 10-4, suppose α = 0.10. Which of the following represents the result of the
relevant hypothesis test?
a)The alternative hypothesis is rejected.
b)The null hypothesis is rejected.
c)The null hypothesis is not rejected.
d)Insufficient information exists on which to make a decision.
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: pooled variance, t test, decision
44.Referring to Table 10-4, suppose α = 0.05. Which of the following represents the result of the
relevant hypothesis test?
a)The alternative hypothesis is rejected.
b)The null hypothesis is rejected.
c)The null hypothesis is not rejected.
d)Insufficient information exists on which to make a decision.
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: pooled variance, t test, decision
45.Referring to Table 10-4, suppose α = 0.01. Which of the following represents the result of the
relevant hypothesis test?
a)The alternative hypothesis is rejected.
b)The null hypothesis is rejected.
c)The null hypothesis is not rejected.
d)Insufficient information exists on which to make a decision.
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: pooled variance, t test, decision
46.Referring to Table 10-4, suppose α = 0.1. Which of the following represents the correct
conclusion?
a)There is not enough evidence that, on average, families in Gotham have been living in
their current homes for less time than families in Metropolis have.
b)There is enough evidence that, on average, families in Gotham have been living in their
current homes for less time than families in Metropolis have.
c)There is not enough evidence that, on average, families in Gotham have been living in
their current homes for no less time than families in Metropolis have.
Two-Sample Tests and One-Way ANOVA 313
d)There is enough evidence that, on average, families in Gotham have been living in their
current homes for no less time than families in Metropolis have.
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: pooled variance, t test, conclusion
47.Referring to Table 10-4, suppose α = 0.05. Which of the following represents the correct
conclusion?
a)There is not enough evidence that, on average, families in Gotham have been living in
their current homes for less time than families in Metropolis have.
b)There is enough evidence that, on average, families in Gotham have been living in their
current homes for less time than families in Metropolis have.
c)There is not enough evidence that, on average, families in Gotham have been living in
their current homes for no less time than families in Metropolis have.
d)There is enough evidence that, on average, families in Gotham have been living in their
current homes for no less time than families in Metropolis have.
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: pooled variance, t test, conclusion
48.Referring to Table 10-4, suppose α = 0.01. Which of the following represents the correct
conclusion?
a)There is not enough evidence that, on average, families in Gotham have been living in
their current homes for less time than families in Metropolis have.
b)There is enough evidence that, on average, families in Gotham have been living in their
current homes for less time than families in Metropolis have.
c)There is not enough evidence that, on average, families in Gotham have been living in
their current homes for no less time than families in Metropolis have.
d)There is enough evidence that, on average, families in Gotham have been living in their
current homes for no less time than families in Metropolis have.
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: pooled variance, t test, conclusion
49.Referring to Table 10-4, what is the 99% confidence interval estimate for the difference in the
two means?
ANSWER:
-25.54 to -4.46 months
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: confidence interval, difference between two means
50.Referring to Table 10-4, what is the 95% confidence interval estimate for the difference in the
two means?
ANSWER:
-23.00 to -7.00 months
314 Two-Sample Tests and One-Way ANOVA
TYPE: PR DIFFICULTY: Moderate
KEYWORDS: confidence interval, difference between two means
TABLE 10-5
To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.
Exam Score Exam Score
Student Before Course (1) After Course (2)
1 530 670
2 690 770
3 910 1,000
4 700 710
5 450 550
6 820 870
7 820 770
8 630 610
51.Referring to Table 10-5, the number of degrees of freedom is
a)14.
b)13.
c)8.
d)7.
ANSWER:
d
TYPE: MC DIFFICULTY: Easy
KEYWORDS: t test, mean difference, degrees of freedom
52.Referring to Table 10-5, the value of the sample mean difference is _______ if the difference
scores reflect the results of the exam after the course minus the results of the exam before the course.
a)0
b)50
c)68
d)400
ANSWER:
b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: t test, mean difference, test statistic
53.Referring to Table 10-5, the value of the standard error of the difference scores is
a)65.027
b)60.828
Two-Sample Tests and One-Way ANOVA 315
c)22.991
d)14.696
ANSWER:
c
TYPE: MC DIFFICULTY: Easy
KEYWORDS: t test, mean difference, standard error
54.Referring to Table 10-5, what is the critical value for testing at the 5% level of significance
whether the business school preparation course is effective in improving exam scores?
a) 2.365
b) 2.145
c) 1.761
d) 1.895
ANSWER:
d
TYPE: MC DIFFICULTY: Easy
KEYWORDS: t test, mean difference, critical value
55.Referring to Table 10-5, at the 0.05 level of significance, the decision for this hypothesis test
would be:
a)reject the null hypothesis.
b)do not reject the null hypothesis.
c)reject the alternative hypothesis.
d)It cannot be determined from the information given.
ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: t test, mean difference, decision
56.Referring to Table 10-5, at the 0.05 level of significance, the conclusion for this hypothesis test
would be:
a)the business school preparation course does improve exam score.
b)the business school preparation course does not improve exam score.
c)the business school preparation course has no impact on exam score.
d)It cannot be drawn from the information given.
ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: t test, mean difference, conclusion
57.True or False: Referring to Table 10-5, one must assume that the population of difference scores
is normally distributed.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
316 Two-Sample Tests and One-Way ANOVA
KEYWORDS: t test, mean difference, assumption
58.Referring to Table 10-5, the calculated value of the test statistic is ________.
ANSWER:
2.175
TYPE: FI DIFFICULTY: Easy
KEYWORDS: t test, mean difference, test statistic
59.Referring to Table 10-5, the p-value of the test statistic is ________.
ANSWER:
0.0331 (using Excel) or …between 0.025 and 0.05? (using Table E.3 with 7 degrees of freedom)
TYPE: FI DIFFICULTY: Moderate
EXPLANATION: p-value obtained from Excel
KEYWORDS: t test, mean difference, p-value
60.True or False: Referring to Table 10-5, in examining the differences between related samples we
are essentially sampling from an underlying population of difference "scores."
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: t test, mean difference, sampling distribution
61.True or False: The sample size in each independent sample must be the same if we are to test for
differences between the means of 2 independent populations.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: pooled variance, t test, sample size
62.True or False: When we test for differences between the means of 2 independent populations, we
can only use a two-tailed test.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: pooled variance, t test, rejection region
63.True or False: When testing for differences between the means of 2 related populations, we can
use either a one-tailed or two-tailed test.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: t test, mean difference, rejection region
Two-Sample Tests and One-Way ANOVA 317 64.True or False: Repeated measurements from the same individuals is an example of data collected
from 2 related populations.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: t test, mean difference
65.True or False: The test for the equality of 2 population variances assumes that each of the 2
populations is normally distributed.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: F test, difference between two variances, assumption
66.True or False: For all two-sample tests, the sample sizes must be equal in the 2 groups. ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: sample size
67.True or False: When the sample sizes are equal, the pooled variance of the 2 groups is the
average of the 2 sample variances.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: pooled variance, t test, sample size
68.True or False: The F distribution is symmetric.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: F distribution, properties
69.True or False: The F distribution can only have positive values.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS: F distribution, properties
70.True or False: All F tests are one-tailed tests.
ANSWER:
318 Two-Sample Tests and One-Way ANOVA
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: F distribution, properties
71. True or False: A resear cher is curious about the effect of sleep on students? test performances.
He chooses 60 students and gives each 2 tests: one given after 2 hours? sleep and one after 8 hours? sleep. The test the researcher should use would be a related samples test.
ANSWER: True
TYPE: TF DIFFICULTY: Easy KEYWORDS: t test, mean difference
72. When testing H 0: μ1–μ2=0 versus H 1: μ1–μ2≠0, the observed value of the Z -score
was found to be – 2.13. The p -value for this test would be
a) 0.0166. b) 0.0332. c) 0.9668. d) 0.9834.
ANSWER: b
TYPE: MC DIFFICULTY: Easy
KEYWORDS: Z test, difference between two means, p -value
73. When testing 012: 0H μμ-≤ versus 112: 0H μμ->, the observed value of the Z -score was
found to be – 2.13. The p -value for this test would be
a) 0.0166. b) 0.0332. c) 0.9668. d) 0.9834.
ANSWER: d
TYPE: MC DIFFICULTY: Moderate
KEYWORDS: Z test, difference between two means, p -value
74. When testing 012: 0H μμ-≥ versus 112: 0H μμ-<, the observed value of the Z -score was
found to be – 2.13. The p -value for this test would be
a) 0.0166. b) 0.0332. c) 0.9668. d) 0.9834.
Two-Sample Tests and One-Way ANOVA 319 ANSWER:
a
TYPE: MC DIFFICULTY: Easy
KEYWORDS: Z test, difference between two means, p-value
75.True or False: A statistics professor wanted to test whether the grades on a statistics test were the
same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test and found out that the variances were equal. For this situation, the professor should use a t test with related samples.
ANSWER:
False
TYPE: TF DIFFICULTY: Easy
KEYWORDS: pooled variance, t test
76.True or False: A statistics professor wanted to test whether the grades on a statistics test were the
same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test and found out that the variances were equal. For this situation, the professor should use a t test with independent samples.
ANSWER:
True
TYPE: TF DIFFICULTY: Easy
KEYWORDS:pooled variance, t test
77.True or False: A Marine drill instructor recorded the time in which each of 11 recruits completed
an obstacle course both before and after basic training. To test whether any improvement
occurred, the instructor would use a t-distribution with 11 degrees of freedom.
ANSWER:
False
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: t test, mean difference, degrees of freedom
78.True or False: A Marine drill instructor recorded the time in which each of 11 recruits completed
an obstacle course both before and after basic training. To test whether any improvement
occurred, the instructor would use a t-distribution with 10 degrees of freedom.
ANSWER:
True
TYPE: TF DIFFICULTY: Moderate
KEYWORDS: t test, mean difference, degrees of freedom
TABLE 10-6