00:02
Hello students, according to the given question we have to find the confidence interval.
00:07
So they have given sample size n is equal to 1500.
00:12
So in the a bit we have to find p cap that is point estimate that is x divided by n which is equal to 460 by 1500 which is equal to 0 .3067 that is 0 .307.
00:30
In the b bit we have to find 90 % confidence interval for p.
00:36
Here the z critical value is 1 .645 at 90%.
00:44
Confidence interval is equal to p -caf plus or minus z critical value into p -caf into 1 minus p -caf is divided by n into square root.
00:56
By substituting we get 0 .307 plus or minus 1 .645 into square root of 0 .307 into 1 minus 0 .307 divided by 1 ,500, which is equal to 0 .307 plus or minus 0 .096, which is equal to 0 .287, which is equal to 0 .287, 0 .387, 0 .327 ,000.
01:26
Now for 99 % confidence interval, z critical value will be 2 .58.
01:35
So confidence interval is equal to 0 .307 plus or minus 2 .58 into square root of 0 .307 into 1 minus 0 .307 divided by 1500.
01:50
So which is equal to 0 .307 plus or minus 0 .307.
01:56
0 .0307.
01:58
So 99 % confidence interval will be equal to 0 .276 comma 0 .338...