00:01
Hello students in this question it is asked to do a two sample test for the given data.
00:08
For that, first we need degrees of freedom.
00:13
So the formula to find degrees of freedom is s1 squared divided by n1 plus s2 squared divided by n2 whole square divided by s1 squared divided by n2 whole square divided by s1 squared divided by n1 square divided by n1 minus 1 plus s 2 squared divided by n 2 whole square divided by n 2 minus 1 so substituting the values here will be getting degrees of freedom as 24 and the formula to find t statistic is t equals to x1 bar minus minus x2 bar divided by square root of s1 squared divided by n1 less s2 square divided by n2.
01:19
Now substituting the values here 4 .75 minus 5 .18 divided by square root of 0 .2 square 15 plus 0 .3 square divided by 15 and that is equal to minus 4 .6189.
01:52
And here, p value is 0 .0001 and it is given alpha equal to 0 .025.
02:03
So here t critical value is minus 2 .0 .0.
02:10
So here we can observe that p value is less than alpha.
02:17
Therefore we reject h0 and for the next question the degrees of freedom is same formula we are using that is 5 squared divided by 22 plus 7 square divided by 19 whole square divided by 5 square divided by 22 whole square divided by 21 plus 7 square divided by 19 whole square and that is equal to 32 and here test statistic same formula x 1 bar minus x2 bar divided by square root of s 1 square by 8.
03:21
N1 plus s 2 by n2.
03:23
So substituting the values, 25 minus 33 divided by square root of 5 squared divided by 22 less 7 square divided by 19.
03:40
And that is equal to minus 4 .1504.
03:45
And here, p value is 2 into probability of t less than minus 4 .1504.
03:56
And that is equal to 0 .0002...