Some political commentators have remarked that citizens of the United States are increasingly conservative, so much so that many treat "liberal" as a dirty word. We can study political ideology by analyzing responses in the 2006 General Social Survey (the same data we used for Problem Set 5). The variable of interest is: polviews. We want to know if on average Americans are ideological or if they tend to be moderate.
A) Provide a nicely formatted histogram for the distribution of responses. Provide the sample mean and standard deviation, explaining in words what these estimates mean substantively about American ideology.
B) You will conduct a significance test for how the population mean, μ, compares to the moderate value on the seven point ideology scale using the a= 0:05 threshold. State your null and alternative hypotheses.
C) Using the Normal approximation, what is the rejection region for your test statistic? What values of the sample mean would lead to rejection (that is, what values of the sample mean would produce test statistics that would fall in the rejection region)? Now, using the t-distribution, what is the rejection region for the test statistic? How similar or different are these rejection regions? Why?
D) After using STATA to identify the sample mean, the sample standard deviation, and the sample size, calculate by hand: 1) the standard error of the sample mean, and 2) the test statistic (showing formulas and your work).
E) Based on your test can we conclude that Americans are moderate on average? Explain.
F) Let's say that you decided to dig deeper and do similar hypothesis test for each of sixty separate policy questions finding three are significant at the 0.05 level. Why would it be a bad idea to write a paper just about attitudes on these three "significant" results while ignoring the other 57 "not significant" results"?
G) Suppose we use the scores -3, -2, -1, 0, 1, 2, and 3 instead of the scores 1, 2, 3, 4, 5, 6, and 7 used above. We then test the null hypothesis that μ = 0. Explain the effect of the change in the scores on the sample mean, the sample standard deviation, the test statistic, and the p-value.