Second six weeks review
name _______________________________
1. The mean height of American women in their early twenties is about 64.5 inches and the standard deviation is
about 2.5 inches. The mean height of men the same age is about 68.5 inches, with standard deviation about 2.7
inches. If the correlation between the heights of husbands and wives is about r = 0.5, what is the slope of the
regression line of the husband’s height on the wife height in young couples? Graph this data on the calculator and
compute the regression line (state it below). Predict the height of the husband of a woman who is 67 inches tall.
2. Lydia and Bob were searching the Internet to find information on air travel in the United States. They found data
on the number of commercial aircraft flying in the United States during the years 1990-1998. The dates were
recorded as years since 1990. Thus, the year 1990 was recorded as year 0. They fit a least squares regression line to
the data. The graph of the residuals and part of the computer output for their regression are given below.
^
y  2939.93  233.517 x
r = 0.88
A. Is a line an appropriate model to use for these data?
tells you this?
What information
Scatter Plot
Aircraft
50
B. What is the predicted number of commercial aircraft flying in 1995?
Residuals
30
10
-10
C. What was the actual number of commercial aircraft flying in 1995?
-30
-50
1
2
3
4
5
6
7
Years_Since_1990
3. It is usual in finance to describe the returns from investing in a single stock by regressing the stock’s returns on
the returns from the stock market as a whole. This helps us see how closely the stock follows the market. We
analyzed the monthly percent total return y on Philip Morris common stock and the monthly return x on the Standard
& Poor’s 500 Index, which represents the market, for the period between July 1990 and May 1997. Here are the
results:
x  1.304 sx  3.392 r  0.5251
y  1.878 s y  7.554
A scatterplot shows no very influential observations.
A. Find the equation of the least-squares line from this information.
B. What percent of the variation in Philip Morris stock is explained by the linear relationship with the market
as a whole?
4. The effect of removing the right-most point (near the positive x-axis) in the scatterplot shown would be:
(a) The slope of the LSRL will increase; r will increase
(b) The slope of the LSRL will increase; r will decrease
(c) The slope of the LSRL will decrease; r will increase
(d) The slope of the LSRL will decrease; r will decrease
(e) No change
8
9
5. A student project measured the increase in the heart rates of fellow students when they stepped up and down for
three minutes to the beat of a metronome. The step was either 5.75 or 11.5 inches high and the metronome beat was
14, 21, or 28 steps per minutes. Thirty students were involved in the project.
a. What are the experimental units or subjects?
b. What is the factor(s)?
c. How many levels? _____
d. What is the response variable?
e. Use a diagram to describe a completely randomized experimental design.
6. 10% of adults belong to health clubs, and 40% of these health club members go to the club at least twice a week.
What percent of all adults go to a health club at least twice a week? Write the information in terms of probabilities
and use the general multiplication rule.
7. Independence of events is not always obvious. Toss two balanced coins independently. The four possible
combinations of heads and tails in order each have probability 0.25. The events A = head on the first toss and B =
both tosses have the same outcome may seem intuitively related. Show that P(B | A) = P(B), so that A and B are in
fact independent.
8. The distribution of blood types in China and the U.S. distribution are given:
Blood type
O
A
B
China
probability
0.35
0.27
0.26
Blood type
O
A
B
0.45
0.40
0.11
U.S. probability
AB
AB
Choose an American and a Chinese at random, independently of each other.
A. Find the missing percentage in each distribution. What is the sum of each distribution?
B. What is the probability that both have type O blood?
C. What is the probability that both have the same blood type?
11. Doctors identify “chronic tension-type headaches” as headaches that occur almost daily for at least six months.
Can antidepressant medications or stress management training reduce the number and severity of these headaches?
Are both together more effective than either alone? Investigation compared four treatments: antidepressant alone,
placebo alone, antidepressant plus stress management, and placebo plus stress management. The headache sufferers
named in the following table have agreed to participate in the study.
Acosta
Duncan
Han
Liang
Padilla
Valasco
Ashiro
Durr
Howard
Maldonado
Plochman
Vaughn
Bennett
Edwards
Hruska
Marsden
Rosen
Wei
Bikalis
Farouk
Imrani
Montoya
Solomon
Wilder
Chen
Fleming
James
O’Brian
Trujillo
Willis
Clemente
George
Kaplan
Ogle
Tullock
Zhang
A. Number the sufferers alphabetically and outline the design of the experiment. What is this type of design called?
B. Using line 113 of your random digits table, who would be in Group 1?