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Exercises 257

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 differ-
ence 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 educa-
tion on the educational attainment of her children. The researcher col-
lects 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).

6.8 A government study found that people who eat chocolate frequently weigh
less than people who don’t. Researchers questioned 1000 individuals from
California between the ages of 20 and 85 about their eating habits, and
measured their weight and height. On average, participants ate choco-
late twice a week and had a body mass index (BMI) of 28. There was an
observed difference of five to seven pounds in weight between those who
ate chocolate five times a week and those who did not eat any chocolate at
all, with the chocolate eaters weighing less on average. Frequent chocolate
eaters also consumed more calories, on average, than people who con-
sumed less chocolate. Based on this summary, would you recommend that
American’s who do not presently eat chocolate, consider eating chocolate
up to five times a week if they want to lose weight? Why or why not?
Explain.

6.9 (Yi, X1i, X2i) satisfy the assumptions in Key Concept 6.4. You are interested
in b1, the causal effect of X1 on Y. Suppose that X1 and X2 are uncorrelated.
You estimate b1 by regressing Y onto X1 (so that X2 is not included in the
regression). Does this estimator suffer from omitted variable bias? Explain.