Chapter 7.2, Problem 44E

To determine

The correct answer from the options that the standard deviation of the sampling distribution is about (a) 0.0006, (b) 0.033, (c) 0.017, (d) 1, (e) none of these.

Answer to Problem 44E

The correct answer is (c).

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 standard deviation of the sampling distribution of $\widehat{p}$is, ${\sigma }_{\widehat{p}}=\sqrt{\frac{p\left(1-p\right)}{n}}$ .

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 standard deviation of the sampling distribution of $\widehat{p}$is ${\sigma }_{\widehat{p}}=\sqrt{\frac{p\left(1-p\right)}{n}}$ .

Substitute 0.30 for pand 750 for nin the above formula.

  $\begin{array}{c}{\sigma }_{\widehat{p}}=\sqrt{\frac{0.30\left(1-0.30\right)}{750}}\\ =\sqrt{\frac{0.30\times 0.70}{750}}\\ =\sqrt{\frac{0.21}{750}}\\ \approx 0.017\end{array}$

Hence, the correct answer is (c).