00:01
Hello everyone we are going to solve a question and then in this question we are given standard deviation that is sigma 1 is equal to 0 .020 sigma 2 is equal to 0 .025 and n1 equals to n2 equals to 10 this is given and alpha is equals to 0 .05 this is also given so we have to find in first part that is a part we have to find p value when at alpha is 0 .05.
00:32
In next part that is b part we are given that this delta is equal to 0 .04.
00:39
Then we have to find power of this test and in c part we are given that beta is equals to 0 .05 and delta is equals to this 0 .04 and we have to find sample size.
00:53
In this we have to calculate simple size and in this we have to calculate power.
00:58
So let's start with the solution with the a part.
01:03
In a part, firstly we calculate the mean of these.
01:07
So mean of first is equals to 16 .03 plus 16 .04 plus 16 .05 and shown to the mean of the given data which is 16 .02 and the last term is 15 .99 and thus divided by 10 which comes out to be 16 point.
01:29
018.
01:31
Now in the second x2 bar is calculated as 16 .02 plus 15 .9 7 and this is 9 7 show on to the last term is 16 .01 plus 16 .00 and this divided by 10 then the mean is equals to 16 .005.
01:53
So, now we write the null hypothesis and alternative hypothesis which is h0 as mu one is equal to mu two and h a alternative hypothesis is mu one is not equals to mu two.
02:08
So now we find the test statistic that is we calculate the z for calculating the p value.
02:16
So the z is equals to x1 bar minus x1 bar here we have minus x2 bar.
02:24
And this divided by under root sigma 1 square divided by n1 plus sigma 2 square divided by n2...