1. Take a look again at the distribution of support for capital punishment (CAPPUN), this time with what is called a frequency distribution.
a. Click Analyze/Descriptive Statistics/Frequencies.
b. Highlight CAPPUN and click on the arrow that sends it over to the Variables window, then click OK.
Examine the percentages in the Valid percent column. What percentage of the U.S. population in 2016 favored capital punishment?
2. Now select random samples of the GSS2016 or GSS2016x respondents (sorry, but you can’t carry out this exercise if you are using the GSS2016x_reduced file):
a. Go to the Data Editor window, and select a random sample containing 40 of the respondents. From the menu:
b. Click Data/Select cases/Random sample of cases.
c. Choose Sample.
d. For “Sample Size,” choose Exactly and then enter 40 cases from the first 100 cases.
e. Click Continue/OK. (Before you click OK, be sure that the “Filter out unselected cases” box is checked.)
f. Determine the percentage of the subsample that favored capital punishment by repeating the steps in SPSS Exercise 1. Record the subsample characteristics and its percentage.
g. Now, repeat Steps 2a through 2e 10 times. Each time, add 100 to the “first 100 cases” request (so that on the last step you will be requesting “Exactly 40 cases from the first 1,000 cases”).
h. Select a random sample containing five of the respondents. Now repeat Steps 2a through 2f (10 times), this time for samples of 5.
3. How does the distribution of CAPPUN in these subsamples compare with that for the total GSS sample?
a. Plot the percents produced in Step 2g and 2h on separate sheets of graph paper. Each graph’s horizontal axis will represent the possible range of percentages (from 0 to 100, perhaps in increments of 5); the vertical axis will represent the number of samples in each range of percentages (perhaps ranging from 0 to 10). Make an X to indicate this percentage for each sample. If two samples have the same percentage, place the corresponding Xs on top of each other. The X for each sample should be one unit high on the vertical axis.
b. Draw a vertical line corresponding to the point on the horizontal axis that indicates the percentage of the total GSS sample that favors capital punishment.
c. Describe the shape of both graphs. These are the sampling distributions for the two sets of samples. Compare them with each other. Do the percentages from the larger samples tend to be closer to the mean of the entire sample (as obtained in SPSS Exercise 1)? What does this tell you about the relationship between sample size and sampling error?