Each year, Management Accounting reports the results of a salary survey of the members of the Institute of Management Accountants (IMA). One year, the 2,112 members responding had a salary distribution with a 20th percentile of $35,100; a median of $50,000; and an 80th percentile of $73,000.
a. Use this information to determine the minimum sample size that could be used in next year's survey to estimate the mean salary of IMA members to within $2,000 with 98% confidence. [To estimate s, first apply Chebyshev's Theorem to find k such that at least 60% of the data fall within k standard deviations of µ. Then find s ≈ (80th percentile - 20th percentile)/2k.]
b. Explain how you estimated the standard deviation required for the sample size calculation.
c. List any assumptions you make.