Chapter 10.3, Problem 41E

a:

To determine

Calculate the sample size.

Explanation of Solution

Sample size (n) can be calculated as follows.

$\begin{array}{c}\text{Sample size}={\left(\frac{{\text{Z}}_{\text{90\%}}\times \text{Standard deviation}}{\text{Population mean}}\right)}^2\\ ={\left(\frac{1.645\times 50}{\text{10}}\right)}^2\\ =68\end{array}$

Sample size is 68.

b:

To determine

Calculate the new sample size with standard deviation of 100.

Explanation of Solution

Sample size (n) can be calculated as follows.

$\begin{array}{c}\text{Sample size}={\left(\frac{{\text{Z}}_{\text{90\%}}\times \text{Standard deviation}}{\text{Population mean}}\right)}^2\\ ={\left(\frac{1.645\times 100}{\text{10}}\right)}^2\\ =271\end{array}$

Sample size is 271.

c:

To determine

Calculate the sample size with 95% confidence level.

Explanation of Solution

Sample size (n) can be calculated as follows.

$\begin{array}{c}\text{Sample size}={\left(\frac{{\text{Z}}_{\text{95\%}}\times \text{Standard deviation}}{\text{Population mean}}\right)}^2\\ ={\left(\frac{1.96\times 50}{\text{10}}\right)}^2\\ =97\end{array}$

Sample size is 97.

d:

To determine

Calculate the sample size with new population mean.

Explanation of Solution

Sample size (n) can be calculated as follows.

$\begin{array}{c}\text{Sample size}={\left(\frac{{\text{Z}}_{\text{90\%}}\times \text{Standard deviation}}{\text{Population mean}}\right)}^2\\ ={\left(\frac{1.645\times 50}{\text{20}}\right)}^2\\ =17\end{array}$

Sample size is 17.