Ap Statistics Worksheets With Answers Page 16
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234.43 RAISING SAT SCORES A study finds that high school students who take the SAT, enroll in
an SAT coaching course, and then take the SAT a second time raise their SAT mathematics scores
from a mean of 521 to a mean of 561. What factors other than “taking the course causes higher
scores” might explain this improvement?
The effects of coaching are confounded with those of experience. A student who has taken
the SAT once may improve his or her score on the second attempt because of increased
familiarity with the test.
4.44 ECONOMISTS’ EDUCATION AND INCOME There is a strong positive correlation
between years of education and income for economists employed by business firms. (In particular,
economists with doctorates earn more than economists with only a bachelor’s degree.) There is also a
strong correlation between years of education and income for economists employed by colleges and
universities. But when all economists are considered, there is a negative correlation between education
and income. The explanation for this is that business pays high salaries and employs mostly
economists with bachelor’s degrees, while colleges pay lower salaries and employ mostly economists
with doctorates. Sketch a scatterplot with two groups of cases (business and academic) that illustrates
how a strong positive correlation within each group and a negative overall correlation can occur
together.
The plot below is a very simplified (and not very realistic) example—open circles are
economists in business; filled circles are teaching economists. The plot should show positive
association when either set of circles is viewed separately, and should show a large number of
bachelor’s degree economists in business and graduate degree economists in academia.
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