Sampling
Conduct the following tests of difference in means using alpha = .05:
- Are monthly utilities expenditures different for home-owners relative to renters?
- Do first-income earners in location 1 (SW) earn more than the first-income earners of location 3 (NE)?
- Is there a statistically significant difference in the mean indebtedness levels of the households in location 1 (SW) and location 2 (NW)
In answering each of a, b, and c, you are to use the following instructions:
- Start with a test for differences in variances for a, b, c.
- If you CANNOT REJECT the null that the differences are the same, do a test for differences in means using equal variances. But if you REJECT the null that the variances are the same, do a test for differences in means using unequal variances.
- Make sure you explain how you use critical values or p-values to reject or not reject all hypotheses.
Answer questions 1-4 based on your analysis of utility expenditures for home-owners and renters.
1. F-critical is
A) 1.24 so we cannot accept the null.
B) 1.24 so we cannot reject the null.
C) 1.09 so we cannot reject the null.
D) none of the above
2. The F-statistic is calculated as approximately
A) 0.25
B) 1.24
C) 1.09
D) none of the above
3. The absolute value of the t-statistic > t-critical, so we can reject the null at the 5% significance level.
A) True
B) False
4. Which of the following represents the alternative hypothesis for this scenario?
A) HA: rent exp ≠ own exp
B) HA: rent exp = own exp
C) HA: rent exp ≥ own exp
D) none of the above
Answer questions 5-8 based on your analysis of first-income earners in the SW and NE.
5. First-income earners in location 1 (SW) earn more than first income earners in location 3 (NE).
A) True
B) False
6. The t-critical for the one-tailed test conducted in this situation is approximately
A) 3.25
B) 1.97
C) 1.35
D) none of the above
7. Which of the following represents the null hypothesis for this scenario?
A) H0: income1 ≤ income 3
B) H0: income1 ≥ income 3
C) H0: income1 = income 3
D) none of the above
8. The F-statistic is
A) 1.98
B) 1.35
C) 0.42
D) none of the above
Answer questions 9-12 based on your analysis of the mean indebtedness levels of households in the SW and NW.
9. The following test was used for this scenario: t-Test: Two-Sample Assuming Equal Variances.
A) True
B) False
10. We can conclude that debt levels are the same in the two regions.
A) True
B) False
11. For the t-test, the p-value for this scenario is approximately
A) .01000
B) 0.0528
C) 0.0013
D) 0.1000
12. The appropriate null hypothesis can be written as H0: debt location1 = debt location2.
A) True
B) False
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) sJ – sA = 0; H1: sJ – sA ≠ 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
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