Question

More workers What sample size would be required to reduce the standard deviation of the sampling distribution to one-third the value you found in Exercise 36(b)? Justify your answer.

Short answer

Sample size is$135$.

Step-by-step solution

Given Information

It is given that$n=15$

Calculation

Standard deviation is given by ${\sigma }_{\hat{p}}=\sqrt{\frac{p(1-p)}{n}}$

Dividing it by $3$

$\frac{{\sigma }_{\hat{p}}}{3}=\frac{1}{3}\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{1}{9}·\frac{p(1-p)}{n}}=\sqrt{\frac{p(1-p)}{9n}}$

We can see $n$is replaced by $9n$.

It means sample size need to be multiplied by $9$.

$9n=9\left(15\right)=135$

Required sample size is$135$