Answer:
The sample proportion of printers used in small business is:
[tex]\hat{p}=\frac{25}{70}=0.3571[/tex]
The 95% confidence interval for the population proportion of printers that are used in small businesses is:
[tex]\hat{p} \pm z_{\frac{0.05}{2}} \sqrt{\frac{\hat{p}(1-\hat{p})}{n} }[/tex]
Where:
[tex]z_{\frac{0.05}{2}}=1.96[/tex] is the critical value at 0.05 significance level
[tex]\therefore 0.3571 \pm 1.96 \sqrt{\frac{0.3571(1-0.3571)}{70} }[/tex]
[tex]0.3571 \pm 0.1122[/tex]
[tex]\left ( 0.3571 - 0.1122, 0.3571 + 0.1122 \right)[/tex]
[tex]\left(0.245,0.469 \right)[/tex]
Therefore, the 95% confidence interval for the population proportion of printers that are used in small businesses is (0.245 , 0.469)
