Question

Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $20,000 and $40,000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. Given the information in the Microsoft Excel Online file below, construct a spreadsheet to determine how large a sample should be taken for each desired margin of error.

For a margin of error of ± $400, the required sample size is n =

For a margin of error of ± $230, the required sample size is n =

For a margin of error of ± $70, the required sample size is n =

Answer 1

Sample size n = where

z_a/2 is the z-value at a/2 = 0.025 (since confidence level is 95%, a = 100%-95% = 5%; a/2 = 5%/2 = 2.5%)

Reading from the z-table, z_0.025 = 1.96

= population standard deviation

E = |margin of error|

Here, since there is no population data from previous studies and no preliminary sample from which sample standard deviation can be calculated, it is best to use an approximate standard deviation calculated as range of the annual starting salary divided by 4, i.e. (40,000 - 20,000)/4 = 5,000

Using these data points, sample sizes can be calculated as:

		Formula	(za/2*σ/E)^2
Margin of error ('E)	za/2	Standard deviation (σ)	Sample size (n)
400	1.96	5,000	600
230	1.96	5,000	1,816
70	1.96	5,000	19,600