STATISTICS 101 L - Homework 4
Due Friday, February 27, 2004
• Homework is due by 4:00 PM on the due date at 327 Snedecor. You can always hand in your homework
at the end of lecture on Friday.
• You may talk with others about the homework problems but please write your solutions up independently.
• Please answer homework questions in complete sentences. Make sure to
assignment together.
staple the pages of your
• Normally you will have an opportunity to get help on homework during lab.
Reading:
Feb. 6
Feb. 18
Feb. 23
- Feb. 16
- Feb. 20
- Feb. 25
Section 2.3
Sections 2.4, 2.5
Sections 3.1, 3.2
Assignment:
1. Read pages 135-187 of the text and do problems 2.58, 2.61, 2.80 and 2.84.
2. An educational foundation would like to give scholarships to high school seniors who will be successful
in college. The foundation wishes to see if there is a relationship between the score on a verbal
aptitude test and the grade point average (GPA) in college. If there is, the foundation could use the
verbal aptitude test as a predictor of success in college and thus help them decide who should get the
scholarships. The verbal aptitude test is on a scale of 200 to 800 and GPA is on a scale from 0 to 4.
Below is a plot GPA versus the verbal aptitude test score for 50 students randomly selected from all
students at a large public university.
Below are summary data (verbal aptitude test score is X and GPA is Y) for the 49 students excluding
the outlier.
X
X
n = 49
Y = 135.3
X = 29, 674
X
X
r = 0.534
(Y − Ȳ )2 = 16.71
(X − X̄)2 = 246, 074.88
(a) Use the correlation coefficient and the summaries to come up with the least squares regression
line for predicting GPA from verbal aptitude score.
(b) Use the least squares regression line in (a) to predict the college GPA of a student with a verbal
aptitude test score of 700.
(c) How much of the variation in GPA is explained by the linear relationship with verbal aptitude
test score?
(d) Does a high verbal aptitude test score cause a high GPA? If so, explain how you know. If not,
explain why.
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(e) There is a strong negative association between high school rank (rank=1 means that you are the
top student in your high school class) and first year college GPA. Does high school rank cause
first year college GPA? If so, explain how you know. If not, explain why.
3. Read pages 220-241 in the text and do problems 3.10, 3.14, 3.16, and 3.24.
4. The following is excerpted verbatim from an AP article written by Paul Recer on August 31, 2002.
Caffeine, the chemical stimulant in coffee and tea, has been found to lower the risk of skin
cancer in laboratory mice.
A study suggests that a skin lotion spiked with caffeine or with another compound found i
green tea (EGCG) can reduce by more than half the number of cancer tumors on the skin
of hairless mice exposed to brutal levels of ultraviolet radiation, said Dr. Allan Conney, a
professor of cancer and leukemia research at Rutgers University.
To test effects of caffeine on skin cancer, Conney and his colleagues exposed 90 mice to high
levels of ultraviolet radiation twice a day for 20 days. They used a strain of animals, called
hairless mice, commonly used for skin cancer studies.
After the mice got their ultraviolet doses, the animals were divided into three groups. One
group was slathered daily with a solution of acetone and caffeine. Another group received
acetone and EGCG. The third group got skin applications of acetone only. Acetone is an
organic solvent often used on the skin.
At the end of 18 weeks, the three groups of mice were killed, and the level of skin tumor
formation was analyzed.
(a) Is this study an experiment or an observational study? Explain briefly.
(b) What is the response variable?
(c) What is the explanatory variable?
(d) The article says “... the animals were divided into three groups.” What important information is
missing from the description of how groups were formed?
(e) Is there a control group in this study? If yes, which group is it?
(f) Make a diagram (similar to the diagrams on page 233 or 237 of the text) to show how this study
was designed.
R.
5. The following is excerpted verbatim from a package of COLD-EEZE
R
CLINICALLY PROVEN COLD-EEZE
WITH ZIGGT M
R with ZiggT M (Zinc Gluconate Glycine),
The following studies apply only to Cold-Eeze
the only great tasting lozenge proven effective in treating a Common Cold.
A randomized, double-blind placebo study, with 23mg of ionic zinc in a citrus flavored
lozenge, concluded that treatment of a cold with our Patented formula within 48 hours of
the onset resulted in symptom relief and a 42% reduction in the duration of the common
cold.
(a) What is a “randomized, double-blind placebo study”?
(b) What important piece of information is missing from the description of the study?
R study.
(c) Construct a diagram, like the one on page 233 in your text depicting the Cold-Eeze (d) What does the phrase “Resulted in a 42% reduction in the duration of common cold symptoms.”
mean?
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