Question

Let’s continue our analysis of liberals and conservatives, taking a look this time at differences in their educational attainment. We obtain the following information from the 2002 GSS – the average educational attainment for liberals is 13.90 years (SY = 3.27) and the average educational attainment for conservatives is 13.55 years (SY = 2.82). Data are based on 187 liberals and 227 conservative responses.

a. Test the research hypothesis that there is a difference in level of education between liberals and conservatives, set alpha at 0.01.
b. Would your decision have been different if alpha were set at 0.05?

Answer 1

I assume "SY" is your abbreviation for standard deviation (SD).

Z = (mean1 - mean2)/standard error (SE) of difference between means

SEdiff = √(SEmean1^2 + SEmean2^2)

SEm = SD/√(n-1)

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.

I'll let you do the calculations.