A survey is planned to compare salaries of plant managers in two regions. The pl

Question

A survey is planned to compare salaries of plant managers in two regions. The plan is to take a sample of 200 plant managers from each region and ask their annual salaries. Assume that previous sample statistics suggest that sigma_1 = sigma_2 = exist4500. Are the sample sizes sufficient to produce a 99% confidence interval on mu_1 - mu_2 having a width of only exist1800? The sample sizes sufficient because the samples would need to be at least people each, which is the planned sample sizes of 200. (Round up to the nearest whole number as needed.)

Explanation / Answer

here margin of error E=1800/2 =900

std deviation=4500

for 99% CI; z=2.5758

therefore required sample size =2*(z*std deviation/E)2 =~332

the sample sizes not suffciient because the sample size would need to be at least 332 people each which is greater then the planned sample size of 200.

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