Question
{Exercise 8.27 (Algorithmic)}. Annual starting salaries for college graduates with degrees in business administration are generally...
{Exercise 8.27 (Algorithmic)}. Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $40,000 and $50,000. 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)? 3750 How large a sample should be taken if the desired margin of error is as shown below to the nearest whole number)? a. $500? 216 b. $200? c. $100? d. Would you recommend trying to obtain the $100 margin of error? No, sample requires too much time and expense e. When the desired confidence level is fixed, what happens to the sample size as the margin of error is decreased? It increases
Answers
Solution :
Given that,
Population standard deviation =
= 3750
a) Margin of error = E = 500
At 95% confidence level the z is,
= 1 - 95%
Z
sample size = n = [Z
n = [1.96 * 3750 / 500 ]2
n = 216.09
Sample size = n = 217
b) margin of error = E = 200
sample size = n = [Z
n = [1.96 * 3750 / 200 ]2
n = 1350.56
Sample size = n = 1351
c) margin of error = E = 100
sample size = n = [Z
n = [1.96 * 3750 / 100 ]2
n = 5402.25
Sample size = n = 5403
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