Question 1200621
population ratio is assumed to be .3
population standard error is equal to sqrt(.3 * .7 / 15) = .1183215957.
critical z-score at 95% confidence interval is plus or minus z = 1.959963986.
use the z-score formula to find the raw score.
z = (x-m)/s is the z-score formula.
z is the z-score
x is the sample mean proportion.
m is the assumed population mean proportion.
s is the standard error.
on the low side of the 95% confidence interval, the formula becomes:
-1.959963986 = (x - .3) / .1183215957.
solve for x to get x = -1.959963986 * .1183215957 + .3 = .0680939337.
on the high side of the 95% confidence interval, the formula becomes:
1.959963986 = (x - .3) / .1183215957.
solve for x to get x = 1.959963986 * .1183215957 + .3 = .5319060663.
your 95% confidence interval is from .07 to .53.
here's what it looks like on the z-score graph at <a href = "https://davidmlane.com/hyperstat/z_table.html" target = "_blank">https://davidmlane.com/hyperstat/z_table.html</a>
<img src = "http://theo.x10hosting.com/2023/030101.jpg">
the 95% confidence interval is a two tailed confidence interval with an alpha of .05 / 2 = .025 on each end.