social science statistics
posted by mike .
a professor was curious to whether the students in a very large class she was teaching who turned in their first scored differently from the overall mean on the test.The overall mean score on the test was 75 with a standard deviation of 10;the score were approximately normally distributed.The mean score for the first 20 tests was 78.Did the student turning in their tests first score significantly different from the mean at the .05 level.

Z = (mean1  mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√n
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to your Z score. 
yes