Chapter 7.2, Problem 48E

To determine

To find: the multiplication of the standard deviation by.

Answer to Problem 48E

  $\sqrt{2}$

Explanation of Solution

Given:

Current sample size is 750 and it becomes 375

Formula used:

  ${\sigma }_{\widehat{p}}=\sqrt{\frac{p\left(1-p\right)}{n}}$

Calculation:

Current sample size is 750 and it becomes 375 so it means n sample becomes $\raisebox{1ex}{$n$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

  $\begin{array}{c}{\sigma }_{\widehat{p}}=\sqrt{\frac{p\left(1-p\right)}{n}}\\ =\sqrt{\frac{p\left(1-p\right)}{\raisebox{1ex}{$n$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}\\ =\sqrt{\frac{2p\left(1-p\right)}{n}}\\ =\sqrt{2}{\sigma }_{\widehat{p}}\end{array}$

Standard deviation is multiplied by $\sqrt{2}$ .

Hence, the correct option is (b)