00:01
In this problem, we have to use the normal distribution to find a confidence interval for a proportion p.
00:08
So we have proportion p given the relevant sample results and also we have to give the best point estimate for p, the margin of error that is mp, we can say me and the confidence interval.
00:21
So here we have given the confidence level, say 99 % of confidence level interval for fee.
00:30
And we have given p hat p hat is equals to 0 .38 and n is equals to 525 which is sample size now we have to give the answer in round of figure so first we have to find best point estimate then margin error and also 99 % confidence interval so here we can say point estimate so here this would be p bar is p hat is actually 0 % percent and 0 .38 and now we can see this would be simple size so this is simple size is equals to 525 now standard error which we can say s e is equals to this would be square root so here this would be a square root of p cap is multiplied with 1 minus p cap divided with n so here when we put all these values together so this would be under root of 0 .38 is multiplied as 1 minus 0 .38 divided with 525 so this is 525 is equals to this is 0 .0212 and also we can find confidence interval so here we have c i which is confidence interval at 99%.
02:04
So first we would evaluate alpha.
02:06
So alpha is equal to 1 minus this would be 0 .99 so this would be 1 minus 0 .99.
02:14
So this would be 1 0 .99 is equal so 0 .01 now alpha divided with 2 so here alpha divided with 2 is equal to 0 .01 divided with this is 0 .01 is divided with this is divided with 2 is equal to 0 .005.
02:34
And also we can evaluate z subscript c is equals to z, subscript alpha divide with 2 is equal to 0 .0212.
02:46
And now margin of error, which we can say m .e.
02:50
Margin of error is given why z subscript c is multiplied with se.
02:57
So here this would be simply multiplied.
03:00
So this is z say is equals to 2 .58.
03:05
So here this would be z alpha divide with 2 is equals to say this would be 2 .58 actually so 2 .58.
03:13
So this would be equal to 2 .58 is multiplied width.
03:21
This would be 0 .0212 is equals to 0 .055.
03:30
Now we can see here.
03:32
Here we do have the ci, we can say interval, which is confidence interval is, say, this would be 0 .325.
03:44
So here this would be simply confidence interval is p -cap, say this would be p -cap minus z multiplied with s -e and also p -capped plus z multiplied with s -e...