Statistics
posted by Yah .
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?

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/√(n1)
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.