Question

# The sample size necessary to estimate the difference between two population proportions within an error margin...

The sample size necessary to estimate the difference between two population proportions within an error margin E for a confidence level of 1 - a can be derived from the following expression E = z ^ * sqrt rho iq 1 n 1 + p 2 q 2 n 2 replace n with n (assuming both samples are the same size) and replace each of, by 0.5 (since their values ​​are unknown). Then solve for n. n 2 p 1, q 1 p 2 q 2 Use this approach to find the size of each sample if you want to estimate the difference between the proportions of men and women planning to vote in the next presidential election. Suppose you want 99% confidence that your error is not greater than 0.02.

The margin of error is defined as,

Let the sample sizes are equal. i.e

The formula is reduced to,

Let

and

The margin of error = 0.02

The z critical value is obtained from the standard normal distribution table for significance level = 0.01.

Now,

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