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 $45,000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. What is the planning value for the population standard deviation (to the nearest whole number)?

How large a sample should be taken if the desired margin of error is as shown below (to the nearest whole number)?

a. $500? _____ b. $200? _____ c. $100? _____

d. Would you recommend trying to obtain the $100 margin of error?

Yes, the margin of error is good or No, sample require too much time and expense

Explanation / Answer

Result:

Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $30,000 and $45,000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. What is the planning value for the population standard deviation (to the nearest whole number)?

The range rule tells us that the standard deviation of a sample is approximately equal to one fourth of the range of the data. s = (Maximum – Minimum)/4.

s=(45000-30000)/4 =3750

How large a sample should be taken if the desired margin of error is as shown below (to the nearest whole number)?

95% Margin of error = 1.96*standard error=1.96*sd/sqrt(n)

a. $500? _____

1.96 *3750/sqrt(n)=500

n = (1.96*3750/500)^2 =216.09

=216

b. $200? _____

n = (1.96*3750/200)^2 =1350.56

=1351

c. $100? _____

n = (1.96*3750/100)^2 =5402.25

=5402

d. Would you recommend trying to obtain the $100 margin of error?

Yes, the margin of error is good or

Answer: No, sample require too much time and expense

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