Annual starting salaries for college graduates with degrees in business administration are generally expected to have a population standard deviation of $3,000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. How large a sample should be taken if the desired margin of error is (a) [1 pt] $500

A sample of 139 should be taken.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Ztable as such z has a pvalue of .

That is z with a pvalue of , so Z = 1.96.

Now, find the margin of error M as such

In which is the standard deviation of the population and n is the size of the sample.

Population standard deviation of $3,000.

This means that

How large a sample should be taken if the desired margin of error is $500?

A sample of n is needed.

n is found when M = 500. So

Dividing both sides by 500

Rounding up:

A sample of 139 should be taken.