I'm trying to solve this problem for an online practice exam, I can't come up with the same answer as the options given and I'm trying to understand what I'm doing wrong.
The question is asking for a 95% non-conservative confidence interval for a population proportion. The following was given:
x = 460
n = 1368
I calculated the following:
phat = 460/1368 = 0.3362
standard error of phat = Square root of (phat*(1-phat))/n = 0.01
I used the z* table to find that z* = 1.96.
Because it's asking for the non-conservative confidence interval I used the following formula to calculate the confidence interval:
phat +/- z*standard error of phat
Lower = 0.3362 - 0.025 = 0.3112 = 31.52%
Upper = 0.3362 + 0.025 = 0.3613 = 36.13%
After all those calculations I thought I had the right answer, but this is not an option in the selections. I'm given the following options to choose from:
31.07% to 36.19%
26.83% to 32.23%
28.30% to 30.76%
30.93% to 36.33%
And this is where I'm stumped. I've double checked my numbers and formula several times and don't see what I'm doing wrong.
Thank you for helping me figure this out!