Question

Annual starting salaries for college graduates with degrees in business administration are generally expected to be between 30000 and 50000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. 1. What is the planning value for the population standard deviation?2. How large a sample should be taken if the desired margin of error is

a. $500?
b. $200?
c. $100?
3. Would you recommend trying to obtain the $100 margin of error? Explain.

Answer 1

(1) The planning value for the population standard deviation:

`=(50,000-30,000)/(4)`

= 5,000

(2) Given a = 0.05, Z(0.025) = 1.96 (from standard normal table)

`n = ((Z* SD)/(Error)) ^(2)`

(a)

`n = ((1.96* 5,000)/(500)) ^(2)`

n = 384.16

(b)

`n = ((1.96* 5,000)/(200)) ^(2)`

n = 2,401

(c)

`n = ((1.96* 5,000)/(100)) ^(2)`

n = 9,604

(3) No, because the sample size of the study is too larger.