INSTRUCTOR ANSWER GUIDE
,OpenStax Introductory Statistics 2e
Instructor Answer Guide
CHAPTER 1: SAMPLING AND DATA
Exercise 1. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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 patients with the virus
Exercise 2. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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 patients with the virus sampled from researcher A and researcher B.
Exercise 3. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
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patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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 days) patients with the virus live after treatment
Exercise 4. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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 "statistic" refers to in the example for
Researcher A.
Solution the average length of time (in days) patients with the virus from the sample
live after treatment
Exercise 5. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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;
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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 days) patients with the virus live after treatment
Exercise 6. “Number of times per week” is what type of data?
a. qualitative; b. quantitative discrete; c. quantitative continuous
Solution b
Exercise 7. 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 sampling method was
a. simple random; b. systematic; c. stratified; d. cluster
Solution b
Exercise 8. 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 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
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 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. The population is_____________________
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Solution the houses in the neighborhood around the park in San Antonio, Texas.
Exercise 11. Table 1.27 contains the total number of deaths worldwide as a result of
earthquakes over a 13-year period.
Year Total Number of Deaths
1 231
2 21,357
3 11,685
4 33,819
5 228,802
6 88,003
7 6,605
8 712
9 88,011
10 1,790
11 320,120
12 21,953
13 768
Total 823,856
Table 1.27
a. What is the proportion of deaths between Year 8 and Year 13?
b. What percent of deaths occurred before Year 2?
c. What is the percent of deaths that occurred in Year 4 or after Year 11?
d. What is the fraction of deaths that happened before Year 13?
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 Year 11? In Year 5?
Explain.
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.
Exercise 12. 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
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Exercise 13. 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 14. 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 15. 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 16. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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
Complete the tables using the data provided:
Survival Frequency Relative Cumulative Relative
Length (in Frequency Frequency
days)
0.5–6.5
6.5–12.5
12.5–18.5
18.5–24.5
24.5–30.5
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30.5–36.5
36.5–42.5
42.5–48.5
Table 1.28 Researcher A
Survival Frequency Relative Cumulative Relative
Length (in Frequency Frequency
days)
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
Table 1.29 Researcher B
Solution Survival Frequency Relative Cumulative Relative
Length (in Frequency Frequency
days)
0.5–6.5 2 2 0.0500
40
6.5–12.5 5 5 0.1750
40
12.5–18.5 9 9 0.4000
40
18.5–24.5 5 5 0.5250
40
24.5–30.5 7 7 0.7000
40
30.5–36.5 7 7 0.8750
40
36.5–42.5 2 2 0.9250
40
Survival Frequency Relative Cumulative Relative
Length (in Frequency Frequency
days)
42.5–48.5 3 3 1.0000
40
0.5–6.5 3 3 0.0750
40
6.5–12.5 2 2 0.1250
40
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12.5–18.5 11 11 0.4000
40
18.5–24.5 8 8 0.6000
40
24.5–30.5 7 7 0.7750
40
30.5–36.5 5 5 0.9000
40
36.5–45.5 4 4 1
40
Exercise 17. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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 data refers to in the above example for
Researcher A.
Solution values for X, such as 3, 4, 11, and so on
Exercise 18. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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
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List two reasons why the data may differ.
Solution Answers will vary. Sample answer: One reason may be the average age of the
individuals in the two samples. Or, perhaps the drug affects men and women
differently. If the ratio of men and women aren't the same in both sample
groups, then the data would differ.
Exercise 19. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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
Can you tell if one researcher is correct and the other one is incorrect? Why?
Solution No, we do not have enough information to make such a claim.
Exercise 20. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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
Would you expect the data to be identical? Why or why not?
Solution Since the treatment is not the same the data might be different unless neither
treatment has an effect.
Exercise 21. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
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under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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
How might the researchers gather random data?
Solution Take a simple random sample from each group. One way is by assigning a
number to each patient and using a random number generator to randomly
select patients.
Exercise 22. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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
Suppose that the first researcher conducted his survey by randomly choosing
one state in the nation and then randomly picking 40 patients from that state.
What sampling method would that researcher have used?
Solution He has used a simple random sample method.
Exercise 23. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
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CHAPTER 1: SAMPLING AND DATA
Exercise 1. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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 patients with the virus
Exercise 2. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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 patients with the virus sampled from researcher A and researcher B.
Exercise 3. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
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patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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 days) patients with the virus live after treatment
Exercise 4. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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 "statistic" refers to in the example for
Researcher A.
Solution the average length of time (in days) patients with the virus from the sample
live after treatment
Exercise 5. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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;
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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 days) patients with the virus live after treatment
Exercise 6. “Number of times per week” is what type of data?
a. qualitative; b. quantitative discrete; c. quantitative continuous
Solution b
Exercise 7. 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 sampling method was
a. simple random; b. systematic; c. stratified; d. cluster
Solution b
Exercise 8. 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 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
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 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. The population is_____________________
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Solution the houses in the neighborhood around the park in San Antonio, Texas.
Exercise 11. Table 1.27 contains the total number of deaths worldwide as a result of
earthquakes over a 13-year period.
Year Total Number of Deaths
1 231
2 21,357
3 11,685
4 33,819
5 228,802
6 88,003
7 6,605
8 712
9 88,011
10 1,790
11 320,120
12 21,953
13 768
Total 823,856
Table 1.27
a. What is the proportion of deaths between Year 8 and Year 13?
b. What percent of deaths occurred before Year 2?
c. What is the percent of deaths that occurred in Year 4 or after Year 11?
d. What is the fraction of deaths that happened before Year 13?
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 Year 11? In Year 5?
Explain.
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.
Exercise 12. 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
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Exercise 13. 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 14. 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 15. 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 16. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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
Complete the tables using the data provided:
Survival Frequency Relative Cumulative Relative
Length (in Frequency Frequency
days)
0.5–6.5
6.5–12.5
12.5–18.5
18.5–24.5
24.5–30.5
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Instructor Answer Guide
30.5–36.5
36.5–42.5
42.5–48.5
Table 1.28 Researcher A
Survival Frequency Relative Cumulative Relative
Length (in Frequency Frequency
days)
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
Table 1.29 Researcher B
Solution Survival Frequency Relative Cumulative Relative
Length (in Frequency Frequency
days)
0.5–6.5 2 2 0.0500
40
6.5–12.5 5 5 0.1750
40
12.5–18.5 9 9 0.4000
40
18.5–24.5 5 5 0.5250
40
24.5–30.5 7 7 0.7000
40
30.5–36.5 7 7 0.8750
40
36.5–42.5 2 2 0.9250
40
Survival Frequency Relative Cumulative Relative
Length (in Frequency Frequency
days)
42.5–48.5 3 3 1.0000
40
0.5–6.5 3 3 0.0750
40
6.5–12.5 2 2 0.1250
40
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Instructor Answer Guide
12.5–18.5 11 11 0.4000
40
18.5–24.5 8 8 0.6000
40
24.5–30.5 7 7 0.7750
40
30.5–36.5 5 5 0.9000
40
36.5–45.5 4 4 1
40
Exercise 17. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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 data refers to in the above example for
Researcher A.
Solution values for X, such as 3, 4, 11, and so on
Exercise 18. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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
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List two reasons why the data may differ.
Solution Answers will vary. Sample answer: One reason may be the average age of the
individuals in the two samples. Or, perhaps the drug affects men and women
differently. If the ratio of men and women aren't the same in both sample
groups, then the data would differ.
Exercise 19. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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
Can you tell if one researcher is correct and the other one is incorrect? Why?
Solution No, we do not have enough information to make such a claim.
Exercise 20. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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
Would you expect the data to be identical? Why or why not?
Solution Since the treatment is not the same the data might be different unless neither
treatment has an effect.
Exercise 21. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
9 April 12, 2024
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Instructor Answer Guide
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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
How might the researchers gather random data?
Solution Take a simple random sample from each group. One way is by assigning a
number to each patient and using a random number generator to randomly
select patients.
Exercise 22. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
symptoms are alleviated. The following data (in days) 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
Suppose that the first researcher conducted his survey by randomly choosing
one state in the nation and then randomly picking 40 patients from that state.
What sampling method would that researcher have used?
Solution He has used a simple random sample method.
Exercise 23. Studies are often done by pharmaceutical companies to determine the
effectiveness of a treatment program. Suppose that a new drug is currently
under study to address a respiratory virus. It is given to patients once the
patient exhibits symptoms of the virus. Of interest is the average (mean)
length of time in days from the time the patient starts the treatment until the
symptoms are alleviated. Two researchers each follow a different set of 40
patients with the respiratory virus from the start of treatment until the
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