The General Social Survey asks respondents to rate their political views on a seven-point scale, where 1 = extremely liberal, 4 = moderate, and 7 = extremely conservative.

A researcher analyzing data from the 2014 GSS gets software output:

-----------------------------------------------------

Mean estimation Number of obs = 2500 Mean Std. Err. [99.0% Conf. Interval]

PolViews 4.20 0.030 (4.123, 4.277)

-----------------------------------------------------

(a) Show how to construct the confidence interval from the other information provided.

(b) Would the confidence interval be wider, or narrower,

(i) if you constructed a 95% confidence interval? (ii) if you found the 99% confidence interval only for the 411 respondents who called themselves strong Democrat on political party identification (PARTYID), for whom the mean was 3.150 with standard deviation 1.496?

(c) What assumption are you making about the scale of measurement for political ideology when you use the sample mean and standard deviation?