00:01
So for the first part of the problem here, we're asked for the claim.
00:05
So the claim here is that the mean gpa, so mu, is greater than the mean gpa of the day students.
00:16
So we could say that mu n minus mu d is greater than zero.
00:22
And that corresponds to the alternate hypothesis.
00:27
The opposite of the claim would be.
00:32
That mu n minus mu n minus mu d is less than or equal to zero which corresponds to the null hypothesis this test because of the fact that we're checking to see if essentially a difference so i'll call this oh nor that we're testing to see if the difference of the means is greater than zero so alternatively we could think of this as is zero less than d.
01:06
This is going to be a right tail test.
01:17
Find our test statistic here.
01:20
That's going to be mu n minus mu d, the difference in the means, divided by the pooled standard deviation times the square root of 1 over n1 plus 1 over n2, where the pooled standard deviation is equal to the square root of n1 minus 1 times the variance of 1 plus n2 minus 1 times the variance of 2, or you can think of these as n and d for night and day, divided by n1 plus n2.
02:03
Or pardon me, that should be n1 plus n2 minus 2 in the denominator there...