Question

In 2004 the estimated average housing space per person​ (in square​ feet) was 521 in country A but only 501 in country B. Suppose a team of economists and sociologists from an organization plans to reestimate the difference in the mean housing space per person for workers in country A and country B using a 95% confidence interval with a sampling error of 3 square feet. Find the sample sizes required to obtain such an estimate. Assume equal sample sizes of σ2A=σ2B=49.

The sample sizes should be n 1=n 2

​(Round up to the nearest integer as​ needed.)

Answer 1

At 95% confidence interval the critical value is z^* = 1.96

Margin of error = 3

or, z^* * = 3

or, 1.96 * sqrt(49/n1 + 49/n1) = 3

or, 1.96 * sqrt(98/n1) = 3

or, n1 = (1.96 * sqrt(98)/3)^2

or, n1 = 42

n1 = n2 = 42