December 16, 2008
Final Exam — Math 102 / Core 143 CX
Points are in parentheses. An unsimplified answer like 12√3.51 + 6/7 is usually worth more than
23.3, because it is easier to understand where it came from.
1. (25 points) An educational researcher wants to test whether students using a new curriculum
for teaching fractions learn the material better than those using an older curriculum. She
teaches 100 students, chosen at random, by the new method, and then administers a stan-
dardized exam. Long experience has shown that using the old method, students score an
average of 50 on this exam, but her students’ average score is 54, with an SD of 20.
(a) What kind of test (zor tor 2-sample zor χ2) should be used to decide whether the new
curriculum is better than the old?
(b) Find the value of the variable (zor tor χ2) used in this test.
(c) Find the P-value, i.e., the probability that, if the new curriculum were no better than
the old, her students would average 54 or more just by chance.
(d) Should we conclude that the new curriculum results in higher scores than the old?
(e) Suppose another researcher reaches a conclusion that is the opposite of ours. Should we
conclude that his data is “tainted” (i.e., obtained by faulty methods or even perhaps
falsified)?
2. (20 points) The cathat plant has flowers that are either pink, blue or lavender. A genetic
model holds that a single gene controls the color of the flowers, with pure forms (genotypes
p/p or b/b) having pink or blue flowers respectively; but neither is dominant, so that hybrids
(p/b or b/p) have lavender flowers. In an experiment, lavender-flowered cathats are crossed
with each other, and, out of 40 offspring selected at random, 15 have pink flowers, 22 have
lavender flowers and 3 have blue flowers.
(a) What kind of test would be used to decide whether these results are significant evidence
against the genetic model?
(b) In computing the value of the variable (zor tor χ2) used in this test, should we use
the numbers of plants with flowers of each color, or the percentages of each color? Or
doesn’t it matter?
(c) Compute the value of the variable.
(d) Is this data significant evidence against the model?
3. (15 points) An ecologist projects the level Nof a certain nutrient in a stream by using linear
regression on the amount Fof fertilizer used in a few fields near the stream. Suppose the
averages of Fand Nare 3 (tons) and 3.5 (parts per thousand) respectively, with standard
deviations of 2.5 and 2 respectively, and a correlation of 0.3.
(a) What is his regression equation for projecting Nfrom F?.
(b) Roughly how far off should the ecologist expect the projections to be as he makes them
using his equation in (a)?
