00:02
Hi, so we are given that for a sample, the sample size n is equal to 250 and p is given 0 .80.
00:14
So in the a part, we have been asked to state, is the sample size large enough to use the last sample approximation to construct the confidence interval for p.
00:25
So basically, as you can see, since the value of n, which is equal to 250, is greater than 230, so we can apply large sample, large sample approximation, approximation.
00:50
So this is going to be the answer for a part of our question.
00:56
Now let's have a look to the part in which we have to compute the 95 % of confidence interval.
01:05
So 95 % of confidence interval is we have to compute.
01:10
So first of all, let us write down the formula of 1 minus of alpha, 100 % of confidence interval for the given p can be given by the formula of p cap plus minus z of twice of, sorry, it is alpha by 2, critical value of z into the under root over p cap into the bracket 1 minus of p cap divided by the sample size n.
01:45
So basically for 95 % of confidence interval, alpha should become 100 minus 95 will be 5%.
01:56
That means alpha will comes 0 .05 after dividing with 100.
02:02
So clearly you will get z of alpha by 2 is equals to z of 0 .05 by 2 and this value from that table, you will get 1 .96 at this significance level 0 .05.
02:19
Substituting this in above, we get 0 .8 plus minus of 1 .96 times upon root over p cap 0 .8 into 1 minus of p cap 0 .80 divided by the sample size n that is 250...