10 ### Sample Size DiscussionThe sample size needed to estimate the difference between two population proportions to within a margin of error \( E \) with a confidence level of \( 1 - \alpha \) can be found by using the following expression:\[ E = z_{\alpha/2} \sqrt{ \frac{p_1 q_1}{n_1} + \frac{p_2 q_2}{n_2}} \]Where:- \( z_{\alpha/2} \) represents the critical value from the standard normal distribution corresponding to the confidence level.- \( p_1 \) and \( p_2 \) are the population proportions.- \( q_1 \) and \( q_2 \) are the complements of the population proportions (\( q = 1 - p \)).- \( n_1 \) and \( n_2 \) are the sample sizes.To simplify the calculation, \( n_1 \) and \( n_2 \) can be replaced by \( n \) (assuming that both samples have the same size), and \( p_1, q_1, p_2, \) and \( q_2 \) can each be replaced by 0.5 (because their values are not known). Solving for \( n \) in this expression results in:\[ n = \frac{z^2_{\alpha/2}}{2E^2} \]This formula provides a simplified way to determine the necessary sample size for comparative studies between two population proportions. ### Determining Sample Size for Comparing Proportions of Smartphone Ownership**Objective:**To find the size of each sample required to estimate the difference between the proportions of men and women who own smartphones. We aim for a 95% confidence level with an error margin of no more than 0.045.**Instructions:**1. To find the necessary sample size for each group (men and women), use the provided expression in the discussion linked.2. Ensure the sample sizes (for men and women) consist of whole numbers.**Expression for Sample Size:**Click the information icon to view the detailed discussion on how to calculate the required sample size.**Input Fields:**The sample should include:- __ men- __ women(Type whole numbers.)**Notes:**- The margin of error is the allowable deviation from the true population proportion.- Confidence level indicates the degree of certainty that the population parameter lies within the specified interval.For more details, access the full discussion on sample size calculations by clicking the provided link.

The given confidence level is 95% and the margin of error is 0.045.

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 95% confidence that your error is no more than 0.045 Click the icon to view the discussion of sample size. The sample should include men and (Type whole numbers.) women.