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# Regional Differences in Household Savings

For items 1 to 4, select the best statistical analysis technique for the following research topics. Be very precise about your statistical choice. For example, there are several types of t-tests, correlations, and ANOVA tests. Make sure you specify exactly which statistical analysis technique you would use, e.g. One-Way Anova. Note the following abbreviations: IV = independent variable and DV = dependent variable.

1. You want to study regional differences (IV) in household savings (DV measured in dollars.) You randomly select samples of households in the North, East, South, and West.

2. You want to compare differences in pounds of weight loss (DV) for 79 middle age adults before and after they have attended a rigorous exercise class.

3. You wish to test the null hypothesis that age (defined as young = 20 to 30 years old, and middle age = 31 to 50) makes no difference in purchasing one of four makes of cars (DV = Honda, Toyota, Lexus, Chevy). Which statistical test would you conduct?

4. Referring back to item 3, assume the critical value for this test is 6.73, and you obtain a computed statistical value of 11.27. Is there evidence to accept the null hypothesis?

For items 5 to 7: You want to compare the effectiveness of three methods of training (IV) in how to handle interviews with the press. You plan to administer a test (DV measured on an interval scale) to the participants in three different seminars with each seminar using a different training method.

5. State the research hypothesis you are testing.

6. Which sampling method would yield the best representative sample? Write a paragraph of at least six sentences with the rationale for the selecting the sampling design. Cite the source of the sampling design.

7. Which inferential statistical test would you use for the "method of training" case scenario (described above) and why?

For questions 8 and 9: Your employer asks you to determine whether sales of cars (DV) can be predicted from the GDP (Gross Domestic Product).

8. What is the appropriate inferential statistical test for the case scenario?

9. Referring back to item 8, if the computed statistical result is significant, what would you know?

10. You run a two tail t-test. The critical value for this test at the .05 level is a t of 7.82. What value must the obtained t-test statistic be in order to be considered significant at the .05 level?

#### Solution Preview

1. You want to study regional differences (IV) in household savings (DV measured in dollars.) You randomly select samples of households in the North, East, South, and West.

- If you are going to be comparing these groups to see if there is a difference, I would say to use an ANOVA. This is a one way anova specifically since we only have 1 DV

2. You want to compare differences in pounds of weight loss (DV) for 79 middle age adults before and after they have attended a rigorous exercise class.

- I would use a paired t-test in this case, since we are using the same group of people before and after the exercise class.

3. You wish to test the null hypothesis that age (defined as young = 20 to 30 years old, and middle age = 31 to 50) makes no difference in purchasing one of four makes of cars (DV = Honda, Toyota, Lexus, Chevy). Which statistical test would you conduct?

- This would be a factorial ANOVA. We have more then 1 IV, and then we have 4 DVs. This would be a 2 X 4 analysis. This would not be a MANOVA since we only have 1 treatment variable (age).

4. Referring back to item 3, assume the critical value for this test is 6.73, and you obtain a computed statistical value of 11.27. Is there evidence to accept the null hypothesis?

We would use a F-table in this case, and our f-table shows the critical value is 6.73. Since our test statistic is HIGHER then our critical value, we would reject the null hypothesis, and conclude that age does influence our purchasing of cars.

(NOTE: the null hypothesis would state that there should be equal chance of each age group purchasing either car type. Our alternative states that there is a difference in ...

#### Solution Summary

The solution examines regional differences in household savings in the North, South, East and West.

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