Question

A random sample of 70 printers discovered that 25 of them were being used in small businesses. find the 95% limit for the population proportion of printers that are used in small businesses.

Answer 1

Answer:

The sample proportion of printers used in small business is:

$\hat{p}=\frac{25}{70}=0.3571$

The 95% confidence interval for the population proportion of printers that are used in small businesses is:

$\hat{p} \pm z_{\frac{0.05}{2}} \sqrt{\frac{\hat{p}(1-\hat{p})}{n} }$

Where:

$z_{\frac{0.05}{2}}=1.96$ is the critical value at 0.05 significance level

$\therefore 0.3571 \pm 1.96 \sqrt{\frac{0.3571(1-0.3571)}{70} }$

         $0.3571 \pm 0.1122$

         $\left ( 0.3571 - 0.1122, 0.3571 + 0.1122 \right)$

         $\left(0.245,0.469 \right)$

Therefore, the 95% confidence interval for the population proportion of printers that are used in small businesses is (0.245 , 0.469)