Assignment:
Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal, unless your instructor stipulates otherwise.
Confidence Interval for Discrimination Using the sample data shown below, construct a 90% confidence interval estimate of the difference between the mean age of unsuccessful applicants and the mean age of successful applicants. What does the result suggest about discrimination based on age?
Exercise
Hypothesis Test for Discrimination The Revenue Commissioners in Ireland conducted a contest for promotion. Statistics from the ages of the unsuccessful and successful applicants are given below (based on data from "Debating the Use of Statistical Evidence in Allegations of Age Discrimination," by Barry and Boland, American Statistician, Vol. 58, No. 2). Some of the applicants who were unsuccessful in getting the promotion charged that the competition involved discrimination based on age. Treat the data as samples from larger populations and use a 0.05 significance level to test the claim that the unsuccessful applicants are from a population with a greater mean age than the mean age of successful applicants. Based on the result, does there appear to be discrimination based on age?
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Ages of unsuccessful applicants
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n = 23,  = 47.0 years, s = 7.2 years
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Ages of successful applicants
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n = 30, = 43.9 years, s = 5.9 years
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