Is self-employment for immigrant workers a faster route to economic advancement in the country? This was one of the questions studied in research published in the International Journal of Manpower (Vol. 32, 2011). One aspect of the study involved comparing the ages of self-employed and wage-earning immigrants. The researcher found that in Sweden, native wage earners tend to be younger than self-employed natives. However, immigrant wage earners tend to be older than self-employed immigrants. This inference was based on summary statistics for male Swedish immigrants shown in the table.

a. Based on the information given, why is it impossible to provide a measure of reliability for the inference "Self-employed immigrants are younger, on average, than wage-earning immigrants in Sweden"?
b. What information do you need to obtain a measure of reliability for the inference, part a?
c. Give a value of the test statistic that would lead you to conclude that the true mean age of self-employed immigrants is less than the true mean age of wage-earning immigrants if you are willing to risk a Type I error rate of .01.
d. Assume that σ, the standard deviation of the ages, is the same for both self-employed and wage-earning immigrants. Give an estimate of σ that would lead you to conclude that the true mean age of self-employed immigrants is less than the true mean age of wage-earning immigrants using α = .01.
e. Is the true value of a likely to be larger or smaller than the one you calculated in part d?

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Self-Employed Wage-Earning Immigrants Immigrants Sample Size Mean Age (years) 870 84,875 44.88 46.79