Math 1107
Practice test 1
1. The table below shows the data of the percent of females among people earning
doctorates in 1993 in several fields of study:
Computer Science
Life Sciences
Education
Engineering
Physical Sciences
Psychology
14.4%
39.9%
59.9%
9.6%
21.9%
61.2%
(a) Present the data in a well-labeled bar graph.
(b) Would it also be correct to use a pie chart to display these data?
2. There is some evidence that increasing the amount of calcium in the diet can lower
blood pressure. In a medical experiment one group of men was given daily calcium
supplement, while a control group received a placebo, The seated systolic blood
pressure of all the men was measured before the treatments began and again after 12
weeks. The blood pressure distributions in the two groups should have been similar at
the beginning of the experiment. Here are the initial blood pressure readings for the
two groups:
Calcium group
107 110 123 129 112 111 107 112 136 102
Placebo group
123 109 112 102 98 114 119 112 110 117 130
Make a back-to-back stem-and leaf plot of these data and describe the two plots. Does
your plot show any major differences in the two groups before treatments began?
Compare the two plots in terms of shape, center and spread.
3. Here are the percents of the popular vote won by the successful candidate in each
U.S. presidential election from 1948 to 1996:
Year
Percent
Year
Percent
1948 1952 1956 1960 1964 1968 1972 1976 1980 1984 1988
49.6 55.1 57.4 49.7 61.1 43.4 60.7 50.1 50.7 58.8 53.9
1992 1996
43.2 49.2
(a) What is the median percent of the vote won by the successful candidate in
presidential elections?
(b) Call an election a landslide if the winner's percent falls at or above the third quartile.
Which elections were landslides?
4. A consumer advocate conducted a test of two popular gasoline additives, A and B.
There are claims that the use of either of these additives will increase gasoline
mileage in cars. A random sample of 30 cars was selected. Each car was filled with
gasoline and the cars were run under the same driving conditions until the gas tanks
were empty. The distance traveled was recorded for each car. Additive A was
randomly assigned to 15 of the cars and additive B was randomly assigned to the
other 15 cars. The gas tank of each car was filled with gasoline and the assigned
additive. The cars were again run under the same driving conditions until the tanks
were empty. The distance traveled was recorded and the difference in the distance
with the additive minus the distance without the additive for each car was calculated.
The following table summarizes the calculated differences. Note that negative values
indicate less distance was traveled with the additive than without the additive.
Additive
A
B
Values
below Q1
-10, -8, -2
-5, -3, -3
Q1
Median
Q3
1
-2
3
1
4
25
Values
above Q3
5, 7, 9
35, 37, 40
a. Display parallel boxplots of the differences of the two additives.
Two ways that the effectiveness of a gasoline additive can be evaluated are by looking at
either
 The proportion of cars that have increased gas mileage when the additive is used in
those cars, or
 The mean increase in gas mileage when the additive is used in those cars.
b. Which additive, A or B would you recommend if the goal is to increase gas mileage
in the highest proportion of cars? Explain your choice.
c. Which additive, A or B would you recommend if the goal is to have the highest mean
increase in gas mileage? Explain your choice.
Review exercises Part 1 (text, page 129): ex 5, 6, 8, 12, 14, 21, 33.
Chapter 6 (text): page 125: 23, 25, 28, 31, 33, 37.