00:01
Hello students, according to the given question we have to find the test statistic value.
00:09
So in the a bit the proportion p1 cap is equal to 267 divided by 330 that is equal to 0 .81 and proportion p2 cap is equal to 295 divided by 670 that is equal to 0 .44.
00:29
So the proportion p is equal to x1 plus x2 divided by n1 plus n2 that is equal to 267 plus 295 divided by 330 plus 670.
00:44
So p is equal to 0 .56.
00:49
Now the hypothesis is h0 such that p1 is equal to p2, h1 such that p1 is not equal to p2.
00:58
So here alpha is equal to 0 .05.
01:04
Now the statistic z is equal to p1 cap minus p2 cap divided by square root of p into 1 minus p into 1 by n1 plus 1 by n2.
01:16
By substituting z is equal to 0 .81 minus 0 .44 divided by square root of 0 .56 into 1 minus 0 .56 into 1 by 330 plus 1 by 670.
01:36
So that is equal to 11 .083.
01:42
So here z is equal to 11 .083 and z critical value is 1 .96.
01:51
So z is less greater than z critical value and coming to the p value is equal to 0 that is less than alpha.
02:02
So we have to reject h0.
02:05
In the c bit the proportion p1 cap is equal to 149 divided by 330 that is equal to 0 .4515 and proportion p2 cap is equal to 308 is divided by 670 that is equal to 0 .4597...