Chapter 7.2, Problem 43E

To determine

The correct answer from the options that the sampling distribution of $\widehat{p}$has mean (a) 225, (b) 0.30, (c) 0.017, (d) 0, (e) none of these.

Answer to Problem 43E

The correct answer is (b).

Explanation of Solution

Given information:

Size of the random sample, $n=750$

Proportion of Division I athletes who think that these drugs are a problem $=30\%$

Formula used:

The mean of the sampling distribution of $\widehat{p}$is, ${\mu }_{\widehat{p}}=p$ .

Consider that proportion of Division I athletes who think that these drugs are a problem be p and the sample size be n.

Rewrite it as:

  $\begin{array}{c}p=30\%\\ =0.30\end{array}$and $n=750$

Know that the mean of the sampling distribution of $\widehat{p}$is ${\mu }_{\widehat{p}}=p$ .

Substitute 0.30 for p in the above formula.

  ${\mu }_{\widehat{p}}=0.30$

Hence, the correct answer is (b).