Question

Which of the following conditions must be met if you want to use z-procedures to construct a confidence interval for a population proportion?

A. The sample size must be at least 30 (some texts say 50).
B The population must be at least 10 times as large as the sample (some texts say 20).
C. Both npˆ and n(1 − pˆ) must be at least 10 (some texts say greater than 5).

Answer 1

Answer:

A. The sample size must be at least 30 (some texts say 50).

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$, a large sample size, of at least 30, can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$.

So the correct answer is:

A. The sample size must be at least 30 (some texts say 50).