## comparison of means of a quantitave variable

I was asked to do this problem in statistics class.

We wish to know who has better grades, the women or the men of the faculty of communication sciences; so we surveyed 200 women and 200 men, and we found in the case of women a mean of 7.9 and an standard deviation of 2.5; and in the case of men a mean of 7.5 and an standard deviation of 3.
Can we prove with this data that the women of the faculty of communication sciences have higher grades than men?

This is my attempt to solve the problem:

first I added 1 to n1 (which was 200) and then proceeded to do the same with n2, (which was also 200). The result of both additions was 201, so I got the square root for it, which turned out to be 14.8. Since the standard deviation for n1 is 2.5, I multiplied that for 14.8, and got 37. the standard deviation for n2 was 3, so that times 14.8 gave me 44.4. After that I divided 37 by the first mean (7.9), and got 4.1 ; and then I proceeded to do the same for 44.4 with the second mean (7.5), and got 5.92. Finally I multiplied 1.96 by 4.1 and got 8; and multiplied 1.96 by 5.92 and got 11.6.
So it seems that men have higher grades than women.

This was the best I could do with the data I had available; so any help would be kindly appreciated.