Use the expression in the accompanying discussion of sample size to find the size of each sample if you want to estimate the difference between proportions of men and women who own smartphones. Assume that you want $99 \%$ confidence that your error is no more than 0.035 . (1) Click the icon to view the discussion of sample size. The sample should include men and women. (Type whole numbers.)

Step 1 ：We are given that we want a 99% confidence level, which corresponds to a Z-score of approximately 2.576. The desired margin of error is 0.035. We'll use 0.5 for P since we don't have any prior knowledge about the proportion of men and women who own smartphones.

Step 2 ：We can calculate the sample size using the formula: \[n = \frac{{Z^2 \cdot P \cdot (1-P)}}{{E^2}}\] where n is the sample size, Z is the Z-score, P is the estimated proportion, and E is the desired margin of error.

Step 3 ：Substituting the given values into the formula, we get: \[n = \frac{{(2.576)^2 \cdot 0.5 \cdot (1-0.5)}}{{(0.035)^2}}\]

Step 4 ：Solving the above expression, we find that the sample size needed is approximately 1355.

Step 5 ：Final Answer: The sample size needed to estimate the difference between proportions of men and women who own smartphones with 99% confidence and a margin of error of no more than 0.035 is \(\boxed{1355}\).