Testing Hypotheses Involving Means
To complete this assignment, you will need to use SPSS for Windows to analyze the data from the 2006 General Social Survey. (SPSS is available in Anspach 251, at the Woldt computer lab, and in the library.) The data for the assignment are in the file GSS2006.sav.
t-tests
1. Choose an independent variable from the GSS 2006 dataset that has two and only two response options. Either choose this kind of variable or RECODE so that the variable has two options only. Create a hypothesis linking your independent variable and Educational Level (variable name = EDUC).
2. Run the independent samples t-test that lets you determine whether your hypothesis is supported. What are the means for your two subgroups?
3. Are the variances of your two sub-groups equal? How do you know this?
4. Present the appropriate t-statistic, the degrees of freedom, and the significance level (2-tailed) that lets you test whether your hypothesis is supported.
5. What do you conclude from your t-test? Is you hypothesis supported? What leads you to say this?
6. Do problem 12 at the end of Chapter 9, on page 305. (You will need Appendix C in your textbook, the t distribution.)
7. Do problem 14 at the end of Chapter 9, on page 305. (You will need Appendix C in your textbook, the t distribution.)
8. Let's say that the mean GPA for the 1,015 high school seniors in in the Monitoring the Future sample in 2006 who have tried alcohol is 3.08, while the mean GPA for the 366 high school seniors who have not tried alcohol is 3.27. The standard error of the difference in means is .041. What is the t-statistic? Is it statistically significant when the alpha level is .05? Why do you say this? (You will need Appendix C in your textbook, the t distribution.)
9. Create the 99% confidence interval around the difference in mean GPA between those who have and those who have not tried alcohol. Use data from Question 8 to answer this question. Is zero in this confidence interval?
10. I ran an analysis of variance using data from the Monitoring the Future dataset consisting of interviews with high school seniors in 2006. See below. Which hypothesis am I testing here. (Note: One variable is GPA and the other is Happiness Level.)
|
Descriptives |
||||||||
|
Grade Point Average |
||||||||
|
|
N |
Mean |
Std. Deviation |
Std. Error |
95% Confidence Interval for Mean |
Minimum |
Maximum |
|
|
|
Lower Bound |
Upper Bound |
||||||
|
Not Happy |
180 |
2.8278 |
.70490 |
.05254 |
2.7241 |
2.9315 |
1.00 |
4.00 |
|
Pretty Happy |
945 |
3.1145 |
.66966 |
.02178 |
3.0717 |
3.1572 |
1.00 |
4.00 |
|
Very Happy |
304 |
3.2783 |
.60295 |
.03458 |
3.2102 |
3.3463 |
1.00 |
4.00 |
|
Total |
1429 |
3.1132 |
.67227 |
.01778 |
3.0783 |
3.1481 |
1.00 |
4.00 |
|
ANOVA |
|||||
|
Grade Point Average |
|||||
|
|
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
Between Groups |
22.951 |
2 |
11.475 |
26.290 |
.000 |
|
Within Groups |
622.429 |
1426 |
.436 |
|
|
|
Total |
645.380 |
1428 |
|
|
|
11. What do you conclude from the analysis of variance found above? Be explicit about whether the hypothesis is supported and how you know this.
12. Choose another independent variable from the General Social Survey dataset (GSS2006.sav) that has more than two response options, but fewer than six. Either choose this kind of variable or RECODE so that the variable has more than two but fewer than six options. Create a hypothesis linking this independent variable and Educational Level (variable name = EDUC).
13. Run the analysis of variance that lets you determine whether your hypothesis is supported. What are the means for your subgroups?
14. Present the F-statistic, the degrees of freedom, and the significance level that lets you test whether your hypothesis is supported.
15. What do you conclude from your F test? Is you hypothesis supported? What leads you to say this?