Annual starting salaries for college graduates with degrees in business administ

Question

Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $30,000 and $50,000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired.

A. What is the planning value for the population standard deviation?

B. How large a sample should be taken if the desired margin of error is $300? Round your answer to the next whole number.

C. How large a sample should be taken in the desired margin of error is $170?

D. How large a sample should be taken if the desired margin of error is $120?

Explanation / Answer

SolutionA:

planning value for the population standard deviation?

=maximum value-minimum value/4

=50000-30000/4

=20000/4

=5000

planning value for the population standard deviation=$5000

SOlutionB:

smaple size=n

we have

n=(z crit*sigma/margin of error)^2

z crit for 95%=1.96

=(1.96*5000/300)^2

=1067.111

n =1067

Required smaple size=n=1067

SolutionC:

margin of error=170

n=(z crit*sigma/margin of error)^2

z crit for 95%=1.96

=(1.96*5000/170)^2

=3323.18

=3323

Required sample size=n=3323

Solutiond:

margin of error=120

n=(z crit*sigma/margin of error)^2

z crit for 95%=1.96

n=(z crit*sigma/margin of error)^2

=(1.96*5000/120)^2

=6669.4

=6669

Required sample size=n=6669

As margin of error reduced sample size increases.

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