00:01
In this question we're given a table of scores before and after and we're asked to do a repeated measures t -test.
00:12
So repeated measures t -test and we're asked to do it with two tails.
00:23
So a two tailed test with a significance level of 0 .05.
00:31
Now in order to do a repeated measures t -test we need to tabulate the differences here.
00:36
So what we can do is pre minus post and fill that out.
00:44
So 45 minus 28 is 17.
00:47
Then we have 5 minus 1, 11, 1, 13, 12 and 1.
01:03
Now we're going to call these differences d.
01:08
Now what we can do is we can calculate d bar by summing them all up and dividing by n.
01:15
Now in this case we have 1, 2, 3, 4, 5, 6, 7, 8 as n.
01:23
So that gives us d bar is equal to, so let's sum them all up, 17 plus 5 minus 1 plus 11 plus 1 plus 13 plus 12 plus 1.
01:36
Divide that by 8 and we get 7 .375.
01:44
Now let's remember that we can calculate our sample standard deviation for d as the square root 1 over n minus 1 times the sum of the squares minus the sum of d squared divided by n, which is the same as 1 over n minus 1 times the sum of the squares minus n times d bar squared.
02:22
So that's the square root of 1 over 7 times 17 squared plus 5 squared plus 1 squared plus 11 squared plus 1 squared plus 13 squared plus 12 squared plus 1 squared.
02:37
And then take off 8 times 7 .375 squared and that gives us the standard deviation on d is, and let's put that in the middle so it's with the rest of our summary statistics, 6 .7175.
03:04
Okay, so now we've got our summary we can do our t -test...