Modesto Junior College
Department of Mathematics
MATH 134 – Summer 2012
Homework #14
The following problems are recommended problems for Chapter 4 and 5. We will discuss
these problems in class. This problem set will not be collected.
Chapter 4: 4.1, 4.3, 4.10 parts (a) and (b) only, 4.11, 4.13, 4.14, 4.15, 4.16, 4.17, 4.18, 4.19,
4.20, 4.21, 4.24, 4.25, 4.26, 4.36
1. (Sports) An investigator measuring various characteristics of a large group of athletes
some years ago found that the correlation between the weight of a male athlete and
the amount of weight he could lift was 0.60. Say whether each of the statements below
is True of False, and explain briefly in each case.
(a) The average male athlete can lift 60% of his body weight.
(b) If an athlete gains 10 pounds, he can expect to be able to lift an additional 6
pounds.
(c) The more an athlete weighs, on the average the more he can lift.
(d) The more an athlete can lift, on the average the more he weighs.
(e) 60% of an athlete’s lifting ability can be attributed to his weight alone.
2. A college newspaper interviews a psychologist about a proposed system for rating the
teaching ability of faculty members. The psychologist says, “The evidence indicates
that the correlation between a faculty member’s research productivity and his or her
teaching rating is close to zero.” The paper reports this as “Professor McDaniel said
that good researchers tend to be poor teachers, and vice versa.”
(a) Sketch the scatter diagram implied by the psychologist’s statement, assuming no
outliers or nonlinearity are present. (You can draw the “football-shaped ellipse”)
(b) Explain briefly why the newspaper’s report is wrong, and write a sentence in plain
language (without using the word “correlation”) that corrects it.
Read Chapter 5 in Moore’s text to supplement the material covered in class.
Moore’s text: Chapter 5: 5.1, 5.2, 5.5, 5.17, 5.20, 5.22, 5.24, 5.25, 5.31, 5.32, 5.42
1. Pearson and Lee obtained the following results in a study of about 1,000 families:
average height of husband ∼ 68 inches, SD ∼ 2.7 inches
average height of wife ∼ 63 inches, SD ∼ 2.5 inches,
r ∼ 0.25
Predict the height of a wife when the height of her husband is:
(a) 72 inches (b) 64 inches (c) unknown
2. A doctor is in the habit of measuring blood pressure twice. She notices that patients
who are unusually high on the first reading tend to have somewhat lower second readings. She concludes that patients are more relaxed on the second reading. A colleagues
disagrees, pointing out that the patients who are unusually low on the first reading tend
to have somewhat higher second readings, suggesting they get more nervous. Which
doctor is right? Or perhaps both are wrong? Explain briefly.
Note: The following problems include material covered in Moore’s text,
Chapter 23, methods of inference for regression.
3. A regression line for predicting test scores has an r.m.s. error of 8 points.
(a) About 68% of the time, the predictions will be right to within ±
points.
(b) About 95% of the time, the predictions will be right to within ±
points.
4. The data from the father’s height versus son’s height scatter diagram from class can
be summarized as:
average height of fathers ∼ 68 inches, SD ∼ 2.7 inches
average height of sons ∼ 69 inches, SD ∼ 2.7 inches,
r ∼ 0.5
(a) Find the r.m.s. error of the regression line for predicting son’s height from father’s
height.
(b) If a father is 72 inches tall, predict his son’s height.
(c) This prediction is likely to be off by
If more information is needed, say what it is, and why.
(d) Repeat parts (b) and (c), if the father is 66 inches tall.
2
inches or so.