Critique each of the following proposed research plans. Your critique should explain any problems with the proposed research and describe how the research plan might be improved. Include a discussion of any additional data that need to be collected and the appropriate statistical techniques for analyzing the data.
(a) A researcher is interested in determining whether a large aerospace firm is guilty of gender bias in setting wages. To determine potential bias, the researcher collects salary and gender information for all of the firm's engineers. The researcher then plans to conduct a "difference in means" test to determine whether the average salary for women is significantly less than the average salary for men.
(b) A researcher is interested in determining whether time spent in prison has a permanent effect on a person's wage rate. He collects data on a random sample of people who have been out of prison for at least 15 years. He collects similar data on a random sample of people who have never served time in prison. The data set includes information on each person's current wage, education, age, ethnicity, gender, tenure (time in current job), occupation, and union status, as well as whether the person was ever incarcerated. The researcher pins to estimate the effect of incarceration on wages by regressing wages on an indicator variable for incarceration, including in the regression the other potential determinants of wages (education, tenure, union status, and so on).