Instructor Solutions Manual
This instructional material was initially created through a Texas Education Agency (TEA) initiative to provide high-
quality open-source instructional materials to districts free of charge. Funds were allocated by the 84th Texas
Legislature (2015) for the creation of state-developed, open-source instructional materials with the request that
advanced secondary courses supporting the study of science, technology, engineering, and mathematics should be
prioritized.
Chapter 1: SAMPLING AND DATA
Exercise 1 Below is a two-way table showing the types of college sports played by men
and women:
Soccer Basketball Lacrosse Total
Wome 8 8 4 20
n
Men 4 12 4 20
Total 12 20 8 40
Given these data, calculate the marginal distributions of college sports for the
people surveyed.
Solution
Exercise 2 Below is a two-way table showing the types of college sports played by men
and women:
Soccer Basketball Lacrosse Total
Wome 8 8 4 20
n
Men 4 12 4 20
,Statistics
Instructor Solutions Manual
Total 12 20 8 40
Given these data, calculate the conditional distributions for the subpopulation
of women who play college sports.
Solution
Exercise 3. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new viral antibody drug
is currently under study. It is given to patients once the virus's symptoms have
revealed themselves. Of interest is the average (mean) length of time in months
patients live once they start the treatment. Two researchers each follow a
different set of 40 patients with the viral disease from the start of treatment
until their deaths. The following data (in months) are collected.
Researcher A: 3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27;
33; 29; 35; 44; 13; 21; 22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 8; 24;
18; 47; 33; 34
Researcher B: 3; 14; 11; 5; 16; 17; 28; 41; 31; 18; 14; 14; 26; 25; 21; 22;
31; 2; 35; 44; 23; 21; 21; 16; 12; 18; 41; 22; 16; 25; 33; 34; 29; 13; 18; 24;
23; 42; 33; 29
Determine what the key term "population" refers to in the example for
Researcher A.
Solution Viral disease patients.
Exercise 4. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new viral antibody drug
is currently under study. It is given to patients once the virus's symptoms have
revealed themselves. Of interest is the average (mean) length of time in months
patients live once they start the treatment. Two researchers each follow a
different set of 40 patients with the viral disease from the start of treatment
,Statistics
Instructor Solutions Manual
until their deaths. The following data (in months) are collected.
Researcher A: 3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27;
33; 29; 35; 44; 13; 21; 22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 8; 24;
18; 47; 33; 34
Researcher B: 3; 14; 11; 5; 16; 17; 28; 41; 31; 18; 14; 14; 26; 25; 21; 22;
31; 2; 35; 44; 23; 21; 21; 16; 12; 18; 41; 22; 16; 25; 33; 34; 29; 13; 18; 24;
23; 42; 33; 29
Determine what the key term "sample" refers to in the example for Researcher
A.
Solution Viral disease patients sampled from researcher A and researcher B.
Exercise 5. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new viral antibody drug
is currently under study. It is given to patients once the virus's symptoms have
revealed themselves. Of interest is the average (mean) length of time in months
patients live once they start the treatment. Two researchers each follow a
different set of 40 patients with the viral disease from the start of treatment
until their deaths. The following data (in months) are collected.
Researcher A: 3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27;
33; 29; 35; 44; 13; 21; 22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 8; 24;
18; 47; 33; 34
Researcher B: 3; 14; 11; 5; 16; 17; 28; 41; 31; 18; 14; 14; 26; 25; 21; 22;
31; 2; 35; 44; 23; 21; 21; 16; 12; 18; 41; 22; 16; 25; 33; 34; 29; 13; 18; 24;
23; 42; 33; 29
Determine what the key term "parameter" refers to in the example for
Researcher A.
Solution The average length of time (in months) patients live after treatment.
Exercise 6. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new viral antibody drug
is currently under study. It is given to patients once the virus's symptoms have
revealed themselves. Of interest is the average (mean) length of time in months
patients live once they start the treatment. Two researchers each follow a
different set of 40 patients with the viral disease from the start of treatment
until their deaths. The following data (in months) are collected.
,Statistics
Instructor Solutions Manual
Researcher A: 3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27;
33; 29; 35; 44; 13; 21; 22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 8; 24;
18; 47; 33; 34
Researcher B: 3; 14; 11; 5; 16; 17; 28; 41; 31; 18; 14; 14; 26; 25; 21; 22;
31; 2; 35; 44; 23; 21; 21; 16; 12; 18; 41; 22; 16; 25; 33; 34; 29; 13; 18; 24;
23; 42; 33; 29
Determine what the key term "statistic" refers to in the example for
Researcher A.
Solution The average length of time (in months) patients from the sample live after
treatment.
Exercise 7. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new viral antibody drug
is currently under study. It is given to patients once the virus's symptoms have
revealed themselves. Of interest is the average (mean) length of time in months
patients live once they start the treatment. Two researchers each follow a
different set of 40 patients with the viral disease from the start of treatment
until their deaths. The following data (in months) are collected.
Researcher A: 3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27;
33; 29; 35; 44; 13; 21; 22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 8; 24;
18; 47; 33; 34
Researcher B: 3; 14; 11; 5; 16; 17; 28; 41; 31; 18; 14; 14; 26; 25; 21; 22;
31; 2; 35; 44; 23; 21; 21; 16; 12; 18; 41; 22; 16; 25; 33; 34; 29; 13; 18; 24;
23; 42; 33; 29
Determine what the key term "variable" refers to in the example for
Researcher A.
Solution X = the length of time (in months) patients live after treatment
Exercise 8. Number of times per week is what type of data?
a. qualitative; b. quantitative discrete; c. quantitative continuous
Solution b
Exercise 9. A study was done to determine the age, number of times per week, and the
duration (amount of time) of residents using a local park in San Antonio,
Texas. The first house in the neighborhood around the park was selected
randomly, and then the resident of every eighth house in the neighborhood
,Statistics
Instructor Solutions Manual
around the park was interviewed. The sampling method was
a. simple random; b. systematic; c. stratified; d. cluster
Solution b
Exercise 10. A study was done to determine the age, number of times per week, and the
duration (amount of time) of residents using a local park in San Antonio,
Texas. The first house in the neighborhood around the park was selected
randomly, and then the resident of every eighth house in the neighborhood
around the park was interviewed. “Duration (amount of time)” is what type of
data?
a. qualitative; b. quantitative discrete; c. quantitative continuous
Solution c
Exercise 11. A study was done to determine the age, number of times per week, and the
duration (amount of time) of residents using a local park in San Antonio,
Texas. The first house in the neighborhood around the park was selected
randomly, and then the resident of every eighth house in the neighborhood
around the park was interviewed. The colors of the houses around the park
are what kind of data?
a. qualitative; b. quantitative discrete; c. quantitative continuous
Solution a
Exercise 12. A study was done to determine the age, number of times per week, and the
duration (amount of time) of residents using a local park in San Antonio,
Texas. The first house in the neighborhood around the park was selected
randomly, and then the resident of every eighth house in the neighborhood
around the park was interviewed. The population is
______________________
Solution the houses in the neighborhood around the park in San Antonio, Texas.
Exercise 13. Table 1.30 contains the total number of deaths worldwide as a result of
earthquakes from 2000 to 2012.
Year Total Number of Deaths
2000 231
2001 21,357
,Statistics
Instructor Solutions Manual
2002 11,685
2003 33,819
2004 228,802
2005 88,003
2006 6,605
2007 712
2008 88,011
2009 1,790
2010 320,120
2011 21,953
2012 768
Total 823,856
a. What is the proportion of deaths between 2007 and 2012?
b. What percent of deaths occurred before 2001?
c. What is the percent of deaths that occurred in 2003 or after 2010?
d. What is the fraction of deaths that happened before 2012?
e. What kind of data is the number of deaths?
f. Earthquakes are quantified according to the amount of energy they produce
(examples are 2.1, 5.0, 6.7). What type of data is that?
g. What contributed to the large number of deaths in 2010? In 2004? Explain.
h. If you were asked to present these data in an oral presentation, what type of
graph would you choose to present and why? Explain what features you would
point out on the graph during your presentation.
Solution a. 0.5242
b. 0.03%
c. 6.86%
d.
e. quantitative discrete
f. quantitative continuous
g. In both years, underwater earthquakes produced massive tsunamis.
,Statistics
Instructor Solutions Manual
h. Answers may vary. Sample answer: A bar graph with one bar for each year,
in order, would be best since it would show the change in the number of deaths
from year to year. In my presentation, I would point out that the scale of the
graph is in thousands, and I would discuss which specific earthquakes were
responsible for the greatest numbers of deaths in those years.
Exercise 14. Determine the type of sampling used (simple random, stratified, systematic,
cluster, or convenience). A group of test subjects is divided into twelve groups;
then four of the groups are chosen at random.
Solution cluster
Exercise 15. Determine the type of sampling used (simple random, stratified, systematic,
cluster, or convenience). A market researcher polls every tenth person who
walks into a store.
Solution systematic
Exercise 16. Determine the type of sampling used (simple random, stratified, systematic,
cluster, or convenience). The first 50 people who walk into a sporting event
are polled on their television preferences.
Solution convenience
Exercise 17. Determine the type of sampling used (simple random, stratified, systematic,
cluster, or convenience). A computer generates 100 random numbers, and 100
people whose names correspond with the numbers on the list are chosen.
Solution simple random
Exercise 18. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new viral antibody drug
is currently under study. It is given to patients once the virus's symptoms have
revealed themselves. Of interest is the average (mean) length of time in months
patients live once starting the treatment. Two researchers each follow a
different set of 40 patients with the viral disease from the start of treatment
until their deaths. The following data (in months) are collected.
Researcher A: 3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27;
33; 29; 35; 44; 13; 21; 22; 10; 12; 8; 40; 32; 26; 27; 31; 34; 29; 17; 8; 24;
18; 47; 33; 34
,Statistics
Instructor Solutions Manual
Researcher B: 3; 14; 11; 5; 16; 17; 28; 41; 31; 18; 14; 14; 26; 25; 21; 22;
31; 2; 35; 44; 23; 21; 21; 16; 12; 18; 41; 22; 16; 25; 33; 34; 29; 13; 18; 24;
23; 42; 33; 29
Complete the tables using the data provided:
Survival Frequency Relative Cumulative Relative
Length (in Frequency Frequency
months)
0.5–6.5
6.5–12.5
12.5–18.5
18.5–24.5
24.5–30.5
30.5–36.5
36.5–42.5
42.5–48.5
Researcher A
Survival Frequency Relative Cumulative Relative
Length (in Frequency Frequency
months)
0.5–6.5
6.5–12.5
12.5–18.5
18.5–24.5
24.5–30.5
30.5–36.5
36.5–45.5
Researcher B
Solution
Survival Frequency Relative Cumulative Relative
Length (in Frequency Frequency
months)
0.5–6.5 2 0.0500
2
40
, Statistics
Instructor Solutions Manual
6.5–12.5 5 0.1750
5
40
12.5–18.5 9 0.4000
9
40
18.5–24.5 5 0.5250
5
40
24.5–30.5 7 0.7000
7
40
30.5–36.5 7 0.8750
7
40
36.5–42.5 2 0.9250
2
40
42.5–48.5 3 1.0000
3
40
Survival Frequency Relative Cumulative Relative
Length (in Frequency Frequency
months)
0.5–6.5 3 0.0750
3
40
6.5–12.5 2 0.1250
2
40
12.5–18.5 11 0.4000
11
40
18.5–24.5 8 0.6000
8
40