Chapter 12 - Two-Sample Tests
1) True or False: For all two-sample tests, the sample sizes must be equal in the two groups.

2) True or False: When the sample sizes are equal, the pooled variance of the two groups is the average
of the two sample variances.

3) The
t
test for the difference between the means of two independent populations assumes that the
respective
C

4) If we are testing for the difference between the means of two independent populations presuming
equal variances with samples of
n
1
= 20 and
n
2
= 20, the number of degrees of freedom is equal to
B

5) In testing for the differences between the means of two independent populations where the variances
in each population are unknown but assumed equal, the degrees of freedom are
A)
n
- 1.
B)
n
1
+
n
2
- 1.
C)
n
1
+
n
2
- 2.
D)
n
- 2.
Answer:
C

6) In testing for differences between the means of two independent populations, the null hypothesis is:
B

7) In testing for the differences between the means of two independent populations, you assume that the
two populations each follow a ________ distribution.

8)
Given the following information, calculate the degrees of freedom that should be used in the pooled-
variance
t
test.
1

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S
1
2
= 4,
S
2
2
= 6,
n
1
= 16,
n
2
= 25
B

9) Given the following information, calculate
S
p
2
, the pooled sample variance that should be used in the
pooled-variance
t
test.
S
1
2
= 4,
S
2
2
= 6,
n
1
= 16,
n
2
= 25
A)
S
p
2
= 6.00
B)
S
p
2
= 5.00
C)
S
p
2
= 5.23
D)
S
p
2
= 4.00
Answer:
C

10) 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.

11) 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.

TABLE 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
Sample Mean SSATL Score
65.75
79.83
Sample Std. Dev.
11.07
6.41
12) Referring to Table 1, judging from the way the data were collected, which test would likely be most
appropriate to employ?
B

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