Question

Dylan wants to determine a 80 percent confidence interval for the true proportion of high school students in the area who attend their home basketball games. how large of a sample must he have to get a margin of error less than 0.02? [to find n, use the value p* = 1/2 f

Answer 1

He should use a sample size of 655.

We can use the formula

$n=\frac{z_{\alpha\2}^2\hat{p}(1-\hat{p})}{E^2}$

We find the z-value by first subtracting the confidence level from 1:
1 - 0.8 = 0.2

Divide this by 2:
0.2/2 = 0.1

Subtract this from 1:
1 - 0.1 = 0.9

Using a z-table (http://www.z-table.com) we find the z-score associated with this is 1.28.

Now we plug our information into our formula:
$n=\frac{z_{\alpha\2}^2\hat{p}(1-\hat{p})}{E^2} \\ \\=\frac{1.28^2(0.8)(0.2)}{0.02^2} = 655.36$