# (Non-Conservative) Population Proportion Confidence Interval Solution Help Please

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!

• Don't round your intermediate results. In particular, your "0.01" errs substantially because the correct SE is $0.01277\ldots.$ which is over 25% greater. Consider using a continuity correction, too. – whuber May 4 at 11:10
• @whuber thank you for the help - I'm using Excel for the intermediate result so while I typed in the rounded number, in the calculation it's using the 0.1277 number you show as displayed here: 1.96*0.01277=0.025 – Python_Learner_DK May 5 at 7:54
• Then you will come close to just one of the answers--and much closer when you use a continuity correction. – whuber May 5 at 11:17