Q. 43 - The Practice of Statistics for AP

Question

The magazine Sports Illustrated asked a random sample of $750$ Division I college athletes, “Do you believe performance-enhancing drugs are a problem in college sports?” Suppose that $30\%$ of all Division I athletes think that these drugs are a problem. Let $\hat{p}$ be the sample proportion who say that these drugs are a problem.

The sampling distribution of $\hat{p}$ has mean

(a) $225$.

(b) $0.30$.

(c) $0.017$.

(d) $0$.

(e) none of these.

Step-by-Step Solution

Answer

$\text{ (b) }{\mu }_{\hat{p}}=0.30$

Step 1: Given Information

Given

$$\begin{gathered} p=30\% \\ =0.30 \end{gathered}$$

$n=750$

Step 2: Explanation

The population percentage $p$ is equal to the mean of the sampling distribution of the sample proportion $\hat{p}$.

$$\begin{gathered} {\mu }_{\hat{p}}=p \\ =0.30 \end{gathered}$$