When creating a confidence interval for a proportion the conservative margin of error (studied in Chapter 5) and the margin of error found by taking 2 standard errors are closest to each other when
A) the true proportion p is close to 0.
B) the true proportion p is close to 1.
C) the true proportion p is close to .5.
D) the true proportion p is close to the sample proportion $\hat{p}$ .

Question

Quizplus · Accepted Answer

The conservative margin of error and the margin of error found by taking 2 standard errors are closest to each other when the true proportion p is close to .5. This is because the maximum variability (and thus the maximum margin of error) occurs when p = 0.5 in a binomial distribution, which both methods aim to estimate.

When Creating a Confidence Interval for a Proportion the Conservative p^\hat{p}p^​

When Creating a Confidence Interval for a Proportion the Conservative $\hat{p}$