We are asked to determine the sample size to determine the difference in the proportion of men and women who own smartphones with a confidence of 99% and an error of no more than 0.03. If we assume that both samples are equal then we can use the following formula:
[tex]n=\frac{Z^2_{\frac{\alpha}{2}}}{2E^2}[/tex]
Where Z is the confidence and E is the error. Replacing the values we get:
[tex]n=\frac{(0.99)^2}{2(0.03)^2}[/tex]
Solving the operations we get:
[tex]n=544.5\cong545[/tex]
Therefore, each sample of men and women should be of 545.
