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. How large a sample should be taken if the desired margin of error is:

a. $500? Remove all commas from your answer before submitting.

b. $190? Remove all commas from your answer before submitting.

c. $120? Remove all commas from your answer before submitting.

d. Would you recommend trying to obtain the $120 margin of error? Explain.
- Select your answer -Yes, it always better to be more accurate.No, the sample size would probably be too time consuming and costly.

Explanation / Answer

Standard deviation, s = range/4 = (50000-30000)/4 = 5000, For 95% CI z* = 1.96
Formula: Margin of error, E = (1.96 * (s/sqrt(N))

a) 500 = (1.96 * 5000/sqrt(N)), N = (1.96*5000/500)^2 = 384.16 = 385

b) 190 = (1.96 * 5000/sqrt(N)), N = (1.96*5000/190)^2 = 2660.39 = 2661

c) 120 = (1.96 * 5000/sqrt(N)), N = (1.96*5000/120)^2 = 6669.44 = 6670

d) No, the sample size would probably be too time consuming and costly.

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