00:01
The first step on this problem is to find what is u1 minus u2 because that's what the problem is asking for.
00:09
So simply subtract the mean 1, which is 4 .1, minus the second mean, which is 5 .5.
00:16
And this gives us negative 1 .4.
00:21
Now we need to find the standard error of the difference.
00:25
So the standard error of the difference when we have two standard deviations or two means or two samples is equal to the square root of the standard deviation 1, which is 0 .76 squared divided by its sample size of 8, plus the standard deviation of the second sample size, so 2 .51 squared divided by 7.
00:55
We put this into our calculators and we get that the standard error of the difference is 0 .9 860.
01:07
Now that we have the standard error, we need to find the critical t value.
01:13
For the critical t value, we need the degree of freedom and the level of confidence.
01:19
So the level of confidence is 0 .05 because we have a confidence interval of 95%.
01:29
So 1 minus 0 .95 is 0 .05.
01:32
But because we have a confidence we're talking about the means, we need to do a two -tail test.
01:38
So let's divide this degree of freedom of 0 .025.
01:42
So we divided by 2.
01:43
If we find it, if we use a t -table with a two -tail test, we use the alpha value of 0 .05...