00:01
So we have observations and we are going to have our d be the difference between, or a d sub i will be the difference between an x of i minus a y sub i.
00:11
And so our first question we had to determine the values for the d sub i's.
00:16
And so i put these values in and subtract them in a list.
00:20
Next, we want to find what the mean of these values is.
00:24
And the mean of those values is a value of negative.
00:34
1 .6143.
00:35
And the sample standard deviation of those values is 1 .9152.
00:41
So that's quite a few dozen places.
00:43
And we do have a sample size of 7.
00:46
We want to do a hypothesis test to find out, do we have evidence that that difference is below zero? so is a negative difference.
00:55
And we can see it's negative, but is it significantly lower.
00:59
So this is a t value with six degrees of freedom, and we would take the d -d -hat, or the d -bar, i should say, 1 .6 -1 -40, minus the mean we're assuming, divided by that sample standard deviation of those individuals divided by the square root of seven.
01:18
And that t -value is negative 2 .230.
01:22
0 .0.
01:23
And the p value associated with that is the likelihood of being less than or equal to that test statistic.
01:32
And that is a value of 0336.
01:36
And so this is less than a 5 % significance level.
01:42
So we would have evidence to reject the null and therefore conclude that there is sufficient evidence to say the mean...