Lesson 6 Homework Problems
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Conduct the following tests of difference in means using alpha = .05:
 Are monthly utilities expenditures different for homeowners relative to renters?
 Do firstincome earners in location 1 (SW) earn more than the firstincome 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 pvalues to reject or not reject all hypotheses.
Answer questions 14 based on your analysis of utility expenditures for homeowners and renters.
1. Fcritical 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 Fstatistic is calculated as approximately
A) 0.25
B) 1.24
C) 1.09
D) none of the above
3. The absolute value of the tstatistic > tcritical, 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 â‰ own exp
B) HA: rent exp = own exp
C) HA: rent exp â‰¥ own exp
D) none of the above
Answer questions 58 based on your analysis of firstincome earners in the SW and NE.
5. Firstincome earners in location 1 (SW) earn more than first income earners in location 3 (NE).
A) True
B) False
6. The tcritical for the onetailed 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 â‰¤ income 3
B) H0: income1 â‰¥ income 3
C) H0: income1 = income 3
D) none of the above
8. The Fstatistic is
A) 1.98
B) 1.35
C) 0.42
D) none of the above
Answer questions 912 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: tTest: TwoSample 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 ttest, the pvalue 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 onetail 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 ttest 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) ÂµJ  ÂµA â‰¥ 0; H1:ÂµJ  ÂµA < 0
B) ÂµJ  ÂµA â‰¤ 0; H1: ÂµJ  ÂµA > 0
C) ÂµJ  ÂµA = 0; H1: ÂµJ  ÂµA â‰ 0
D) sJ  sA = 0; H1: sJ  sA â‰ 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  
FTest Statistic  2.982491 
Population 1 Sample Degrees of Freedom  210 
Population 2 Sample Degrees of Freedom  99 


TwoTailed Test 

Lower Critical Value  0.719629 
Upper Critical Value  1.419014 
pValue  6.01E09 
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 
tTest Statistic  11.8092 


TwoTailed Test 

Lower Critical Value  1.96767 
Upper Critical Value  1.967669 
pValue  8.22E27 
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 computerrelated purchases via the Internet or store visits. Assume a sample of 8 respondents provided the following data on their computerrelated purchases during a 30day period. Using a .05 level of significance, can we conclude that consumers spend more on computerrelated purchases by way of the Internet than by visiting stores?
 
Respondent  InStore  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 computerrelated 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 Î¼1  Î¼2 < 0
B) null hypothesis should state Î¼1  Î¼2 â‰¤ 0
C) alternative hypothesis should state Î¼1  Î¼2 < 0
D) alternative hypothesis should state Î¼1  Î¼2 > 0
E) both b and d are correct
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