The use of the standard normal distribution for constructing a confidence interval estimate for the population proportion p requires that:
A)n $$\hat { p }$$ and n(1 - $$\hat { p }$$ ) are both greater than 5, where $$\hat { p }$$ denotes the sample proportion.
B)np and n(1 - p) are both greater than 5.
C)n $$\hat { p }$$ and n(p + $$\hat { p }$$ ) are both greater than 5.
D)the sample size is greater than 5.

Question

Quizplus · Accepted Answer

The correct choice is A because for the standard normal distribution (Z-distribution) to be used in constructing a confidence interval for a population proportion, the sample must meet the success-failure condition. This condition requires that the expected number of successes, $n\hat{p}$, and the expected number of failures, $n(1-\hat{p})$, are both greater than 5. This ensures that the sampling distribution of the proportion is approximately normal.

The Use of the Standard Normal Distribution for Constructing a Confidence