Question

The width of a confidence interval estimate for a proportion will be A. narrower for 99% confidence than for 95% confidence. B. wider for a sample size of 100 than for a sample size of 50. C. narrower for 90% confidence than for 95% confidence. D. narrower when the sample proportion is 0.50 than when the sample proportion is 0.20.

Answer 1

C. Narrower for 90% confidence than for 95% confidence.

Explanation:

A limits of a confidence interval are u-E and u+E, where u is the mean and E is the margin of error. The bigger the E the wider the interval is going to be. There is a formula for calculating E for a mean and for a proportion. They are both shown in the picture

A. Is false because the z for a 99% confidence level is greater than the one for a 95% confidence level, so E is going to be larger and the interval is going to be wider.

B. Is false because E decreases as n increases. So the E for 100 is going to be smaller than E for 50 and the interval for 100 is going to be narrower than the one for 50.

D. False because the if we calculate E for p = 0.5 it is going to be bigger than the one for p = 0.20.