6.7 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 those data.

a. A researcher wants to determine whether a leading global university is biased against Black students in admissions. To determine potential bias, the researcher collects race information on all applicants to the university for a given year. The researcher plans to conduct a difference in means test to determine whether the proportion of acceptances among Black candidates is systematically different from the proportion of acceptances among other candidates.

b. A researcher is interested in identifying the impact of a mother’s education on the educational attainment of her children. The researcher collects data on a random sample of individuals aged between 25 and 40 who have exited the schooling system. The data set contains information on each person’s level of schooling, type of school, gender, and ethnicity, as well as information on the schooling of their parents and the demographic characteristics of the household in which they grew up. The researcher plans to regress years of schooling achieved by an individual on the years of schooling of their mother, including as controls in the regression the other potential determinants of schooling (gender, ethnicity, number of siblings, whether parents lived together or were separated).