Statistics

1.

When testing the equality of population variances, the test statistic is the ratio of the sample variances (or equivalently, the ratio of the squared standard deviations).

A) True

B) False

2.

When we test for differences between the means of independent populations, we can only use a one-tail test.

A) True

B) False

3.

The sample size in each independent sample must be the same if we are to test for differences between means.

A) True

B) False

4.

A statistics professor wanted to test whether the grades on a statistics quiz were the same for the online and resident MBA students. The professor took a random sample of 15 students from each course and is going to conduct a test to determine if the VARIANCES in the grades for online and resident MBA students are equal. For this test, the professor should use a t-test with related or matched samples.

A) True

B) False

Situation 6.1.1:

Do Japanese managers have different motivation levels 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. Higher scores indicate more motivation. The SSATL scores are summarized below.

	Japanese Mgrs	American Mgrs
Sample Size	211	100
Mean SSATL Score	65.75	79.83
Population Std. Deviation	11.07	6.41

5.

What is the appropriate null and alternative hypothesis for testing the question posed in Situation 6.1.1?

A) µJ - µA ≥ 0; H1:µJ - µA < 0

B) µJ - µA ≤ 0; H1: µJ - µA > 0

C) µJ - µA = 0; H1: µJ - µA ≠ 0

D) J - A = 0; H1: J - A ≠ 0

6.

Given the following results generated in Excel, are the variances in the sample of Japanese managers different than the variances in the sample of U.S. managers at the .05 level of significance?

Data
Level of Significance	0.05
Population 1 Sample
Sample Size	211
Sample Standard Deviation	11.07
Population 2 Sample
Sample Size	100
Sample Standard Deviation	6.41

Intermediate Calculations
F-Test Statistic	2.982491
Population 1 Sample Degrees of Freedom	210
Population 2 Sample Degrees of Freedom	99

Two-Tailed Test
Lower Critical Value	0.719629
Upper Critical Value	1.419014
p-Value	6.01E-09

A) Yes, there are significant differences in the sample variances.

B) No, there are no significant differences in the sample variances.

7.

Referring to the data, the results of the previous question, and how the data were collected in Situation 6.1.1, which of the following test would be most appropriate to employ?

A) Separate (unequal) variance t test for means.

B) Pooled (equal) variance t test for means

C) Paired or matched sample t test for means

D) F test for variances

8.

If we had been given the following results from Excel (ignoring any previous findings), are motivation levels for Japanese managers different from those of U.S. managers at the .05 level of significance?.

Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	211
Sample Mean	65.75
Sample Standard Deviation	11.07
Population 2 Sample
Sample Size	100
Sample Mean	79.83
Sample Standard Deviation	6.41
Intermediate Calculations
Population 1 Sample Degrees of Freedom	210
Population 2 Sample Degrees of Freedom	99
Total Degrees of Freedom	309
Pooled Variance	96.44709
Difference in Sample Means	-14.08
t-Test Statistic	-11.8092
Two-Tailed Test
Lower Critical Value	-1.96767
Upper Critical Value	1.967669
p-Value	8.22E-27

A) Yes, there is a significant difference in mean SSATL scores.

B) No, there is no significant difference between mean SSATL scores.

Situation 6.1.2:

A survey was recently conducted to determine if consumers spend more on computer-related purchases via the Internet or store visits. Assume a sample of 8 respondents provided the following data on their computer-related purchases during a 30-day period. Using a .05 level of significance, can we conclude that consumers spend more on computer-related purchases by way of the Internet than by visiting stores?

	Expenditures (dollars)
Respondent	In-Store	Internet
1	132	225
2	90	24
3	119	95
4	16	55
5	85	13
6	248	105
7	64	57
8	49	0

9.

Refer to Situation 6.1.2. The test statistic for determining whether or not consumers spend more on computer-related purchases by way of the Internet than by visiting stores is

A) 0.80

B) 1.12

C) 1.76

D) 1.89

10.

If we are interested in testing whether the mean of population 1 is significantly smaller than the mean of population 2, the

A) null hypothesis should state μ1 - μ2 < 0

B) null hypothesis should state μ1 - μ2 ≤ 0

C) alternative hypothesis should state μ1 - μ2 < 0

D) alternative hypothesis should state μ1 - μ2 > 0

E) both b and d are correct