Question

Help with Stats?? Will award and medal!!

A researcher constructs a confidence interval for a population proportion using a sample of size 50. The value of pˆ is .3, and the resulting confidence interval is determined to be (.1323, .4677). What's the level of confidence for this interval?

A. 80%
B. 90%
C. 95%
D. 99%
E. Not enough information to answer

Answer 1

\[.4677=.3+Z\sqrt{\frac{.3(1-.3)}{50}}~~\Rightarrow~~Z=2.59\]
Hmm... I'd have to go with 99%, but I could have sworn the critical value \(Z\) was closer to 2.33...

Answer 2

Actually, the difference in probabilities between 2.33 and 2.59 are on the order of \(10^{-3}\), so it's not a big deal. It's definitely a 99% confidence level.