00:01
So in this question we're testing a claim, but i think due to a formatting error we can't actually tell what that claim is from the question.
00:11
So the claim is going to be either mu1 is less than mu2, mu1 is not equal to mu2, or mu1 is greater than mu2.
00:27
So it's one of those three, we don't know which one it is.
00:31
Two samples are randomly selected.
00:33
We could give a level of significance, alpha is 0 .02.
00:38
Our null hypothesis is going to be that mu1 equals mu2, and our ultimate hypothesis is going to be the claim, whichever what that is.
00:46
And we're given n1 is 51, n2 is 38, x1 bar is 2 .2, x2 bar is 2 .6, sigma1 is 0 .76, and sigma2 is 0 .51.
01:06
So now let's calculate a z statistic.
01:08
So z is going to be x1 bar minus x2 bar divided by the square root of sigma1 squared over n1 plus sigma2 squared over n2.
01:21
And we're using z here because we're told sigma, not s, so these are population standard deviations.
01:27
So what value of z do we get? 2 .2 minus 2 .6 divided by the square root of 0 .76 squared over 51 plus 0 .5 squared over 38 gives us z is minus 2 .9894.
01:48
So that's our z statistic.
01:52
So let's calculate p values.
01:56
The p value is going to depend on the ultimate hypothesis...