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.

Short answer

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

Step-by-step solution

Given Information 

Given

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

$n=750$

Explanation

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

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