00:01
Hello students here from the question we can dictate the null hypothesis and alternative hypothesis like this.
00:08
So the null hypothesis will be mu 1 minus mu 2 is equal to 0 and the alternative hypothesis ha can be stated as mu 1 minus mu 2 not equal to 0.
00:23
Now here we have the given data that is n1 that is the sample size for the first set is 4 and n2 is equal to 8.
00:36
So also the mean m1 is equal to 24 and mean m2 is equal to 14.
00:44
Standard deviation s 1 is equal to 76 and s 2 is equal to 164.
00:51
So here the degree of freedom d f is equal to n1 plus n 2 minus 2.
00:59
So that will be equal to 4 plus 8 minus 2 which is equal to 4 plus 8 minus 2 which is equal to 10.
01:04
So now we have to find the critical value at alpha is equal to 0 .01 and this will be a one tile test.
01:15
So critical value tc will be equal to 2 .763.
01:21
Here the decision rule the decision rule is like this we can reject h node t -note is greater than tc.
01:36
Now, now the pooled variance, sp squared squared variance, sp square is given by n1 minus 1 into s1 square plus n2 minus 1 into s2 square whole divided by df...