Frequency
Relative Frequency
Cumulative
Relative
Frequency
1
30
0.6
2
15
3
Table 1.22
a. Fill in the blanks in the table above.
b. What percent of students take exactly two courses?
c. What percent of students take one or two courses?
Exercise 1.12.3
(Solution on p. 55.)
Sixty adults with gum disease were asked the number of times per week they used to floss before
their diagnoses. The (incomplete) results are shown below:
Flossing Frequency for Adults with Gum Disease
# Flossing per Week
Frequency
Relative Frequency
Cumulative Relative Freq.
0
27
0.4500
1
18
3
0.9333
6
3
0.0500
7
1
0.0167
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Table 1.23
a. Fill in the blanks in the table above.
b. What percent of adults flossed six times per week?
c. What percent flossed at most three times per week?
Exercise 1.12.4
A fitness center is interested in the mean amount of time a client exercises in the center each week.
Define the following in terms of the study. Give examples where appropriate.
a. Population
b. Sample
c. Parameter
d. Statistic
e. Variable
f. Data
Exercise 1.12.5
(Solution on p. 55.)
Ski resorts are interested in the mean age that children take their first ski and snowboard lessons.
They need this information to optimally plan their ski classes. Define the following in terms of the
study. Give examples where appropriate.
a. Population
b. Sample
c. Parameter
d. Statistic
e. Variable
f. Data
Exercise 1.12.6
A cardiologist is interested in the mean recovery period for her patients who have had heart
attacks. Define the following in terms of the study. Give examples where appropriate.
a. Population
b. Sample
c. Parameter
d. Statistic
e. Variable
f. Data
Exercise 1.12.7
(Solution on p. 56.)
Insurance companies are interested in the mean health costs each year for their clients, so that
they can determine the costs of health insurance. Define the following in terms of the study. Give
examples where appropriate.
a. Population
b. Sample
c. Parameter
d. Statistic
e. Variable
f. Data
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CHAPTER 1. SAMPLING AND DATA
Exercise 1.12.8
A politician is interested in the proportion of voters in his district that think he is doing a good
job. Define the following in terms of the study. Give examples where appropriate.
a. Population
b. Sample
c. Parameter
d. Statistic
e. Variable
f. Data
Exercise 1.12.9
(Solution on p. 56.)
A marriage counselor is interested in the proportion the clients she counsels that stay married.
Define the following in terms of the study. Give examples where appropriate.
a. Population
b. Sample
c. Parameter
d. Statistic
e. Variable
f. Data
Exercise 1.12.10
Political pollsters may be interested in the proportion of people that will vote for a particular
cause. Define the following in terms of the study. Give examples where appropriate.
a. Population
b. Sample
c. Parameter
d. Statistic
e. Variable
f. Data
Exercise 1.12.11
(Solution on p. 56.)
A marketing company is interested in the proportion of people that will buy a particular product.
Define the following in terms of the study. Give examples where appropriate.
a. Population
b. Sample
c. Parameter
d. Statistic
e. Variable
f. Data
Exercise 1.12.12
Airline companies are interested in the consistency of the number of babies on each flight, so that
they have adequate safety equipment. Suppose an airline conducts a survey. Over Thanksgiving
weekend, it surveys 6 flights from Boston to Salt Lake City to determine the number of babies on
the flights. It determines the amount of safety equipment needed by the result of that study.
a. Using complete sentences, list three things wrong with the way the survey was conducted.
b. Using complete sentences, list three ways that you would improve the survey if it were to be
repeated.
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Exercise 1.12.13
Suppose you want to determine the mean number of students per statistics class in your state.
Describe a possible sampling method in 3 – 5 complete sentences. Make the description detailed.
Exercise 1.12.14
Suppose you want to determine the mean number of cans of soda drunk each month by persons
in their twenties. Describe a possible sampling method in 3 - 5 complete sentences. Make the
description detailed.
Exercise 1.12.15
(Solution on p. 56.)
771 distance learning students at Long Beach City College responded to surveys in the 2010-
11 academic year. Highlights of the summary report are listed in the table below. (Source:
http://de.lbcc.edu/reports/2010-11/future/highlights.html#focus).
LBCC Distance Learning Survey Results
Have computer at home
96%
Unable to come to campus for classes
65%
Age 41 or over
24%
Would like LBCC to offer more DL courses
95%
Took DL classes due to a disability
17%
Live at least 16 miles from campus
13%
Took DL courses to fulfill transfer requirements
71%
Table 1.24
a. What percent of the students surveyed do not have a computer at home?
b. About how many students in the survey live at least 16 miles from campus?
c. If the same survey was done at Great Basin College in Elko, Nevada, do you think the percent-
ages would be the same? Why?
Exercise 1.12.16
Nineteen immigrants to the U.S were asked how many years, to the nearest year, they have lived
in the U.S. The data are as follows:
2; 5; 7; 2; 2; 10; 20; 15; 0; 7; 0; 20; 5; 12; 15; 12; 4; 5; 10
The following table was produced:
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CHAPTER 1. SAMPLING AND DATA
Frequency of Immigrant Survey Responses
Data
Frequency
Relative Frequency
Cumulative Relative Frequency
0
2
2
0.1053
19
2
3
3
0.2632
19
4
1
1
0.3158
19
5
3
3
0.1579
19
7
2
2
0.5789
19
10
2
2
0.6842
19
12
2
2
0.7895
19
15
1
1
0.8421
19
20
1
1
1.0000
19
Table 1.25
a. Fix the errors on the table. Also, explain how someone might have arrived at the incorrect
number(s).
b. Explain what is wrong with this statement: “47 percent of the people surveyed have lived in
the U.S. for 5 years.”
c. Fix the statement above to make it correct.
d. What fraction of the people surveyed have lived in the U.S. 5 or 7 years?
e. What fraction of the people surveyed have lived in the U.S. at most 12 years?
f. What fraction of the people surveyed have lived in the U.S. fewer than 12 years?
g. What fraction of the people surveyed have lived in the U.S. from 5 to 20 years, inclusive?
Exercise 1.12.17
A “random survey” was conducted of 3274 people of the “microprocessor generation” (people
born since 1971, the year the microprocessor was invented). It was reported that 48% of those
individuals surveyed stated that if they had $2000 to spend, they would use it for computer
equipment. Also, 66% of those surveyed considered themselves relatively savvy computer users.
(Source: San Jose Mercury News)
a. Do you consider the sample size large enough for a study of this type? Why or why not?
b. Based on your “gut feeling,” do you believe the percents accurately reflect the U.S. population
for those individuals born since 1971? If not, do you think the percents of the population are
actually higher or lower than the sample statistics? Why?
Additional information: The survey was reported by Intel Corporation of individuals who visited
the Los Angeles Convention Center to see the Smithsonian Institure’s road show called “America’s
Smithsonian.”
c. With this additional information, do you feel that all demographic and ethnic groups were
equally represented at the event? Why or why not?
d. With the additional information, comment on how accurately you think the sample statistics
reflect the population parameters.
Exercise 1.12.18
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a. List some practical difficulties involved in getting accurate results from a telephone survey.
b. List some practical difficulties involved in getting accurate results from a mailed survey.
c. With your classmates, brainstorm some ways to overcome these problems if you needed to
conduct a phone or mail survey.
1.12.1 Try these multiple choice questions
The next four questions refer to the following: A Lake Tahoe Community College instructor is interested
in the mean number of days Lake Tahoe Community College math students are absent from class during a
quarter.
Exercise 1.12.19
(Solution on p. 56.)
What is the population she is interested in?
A. All Lake Tahoe Community College students
B. All Lake Tahoe Community College English students
C. All Lake Tahoe Community College students in her classes
D. All Lake Tahoe Community College math students
Exercise 1.12.20
(Solution on p. 56.)
Consider the following:
X = number of days a Lake Tahoe Community College math student is absent
In this case, X is an example of a:
A. Variable
B. Population
C. Statistic
D. Data
Exercise 1.12.21
(Solution on p. 56.)
The instructor takes her sample by gathering data on 5 randomly selected students from each
Lake Tahoe Community College math class. The type of sampling she used is
A. Cluster sampling
B. Stratified sampling
C. Simple random sampling
D. Convenience sampling
Exercise 1.12.22
(Solution on p. 56.)
The instructor’s sample produces an mean number of days absent of 3.5 days. This value is an
example of a
A. Parameter
B. Data
C. Statistic
D. Variable
The next two questions refer to the following relative frequency table on hurricanes that have made direct
hits on the U.S between 1851 and 2004. Hurricanes are given a strength category rating based on the
minimum wind speed generated by the storm. (http://www.nhc.noaa.gov/gifs/table5.gif 13)
13http://www.nhc.noaa.gov/gifs/table5.gif
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CHAPTER 1. SAMPLING AND DATA
Frequency of Hurricane Direct Hits
Category
Number of Direct Hits
Relative Frequency
Cumulative Frequency
1
109
0.3993
0.3993
2
72
0.2637
0.6630
3
71
0.2601
4
18
0.9890
5
3
0.0110
1.0000
Total = 273
Table 1.26
Exercise 1.12.23
(Solution on p. 56.)
What is the relative frequency of direct hits that were category 4 hurricanes?
A. 0.0768
B. 0.0659
C. 0.2601
D. Not enough information to calculate
Exercise 1.12.24
(Solution on p. 56.)
What is the relative frequency of direct hits that were AT MOST a category 3 storm?
A. 0.3480
B. 0.9231
C. 0.2601
D. 0.3370
The next three questions refer to the following: A study was done to determine the age, number of times
per week and the duration (amount of time) of resident use of a local park in San Jose. The first house in
the neighborhood around the park was selected randomly and then every 8th house in the neighborhood
around the park was interviewed.
Exercise 1.12.25
(Solution on p. 56.)
“‘Number of times per week”’ is what type of data?
A. qualitative
B. quantitative - discrete
C. quantitative - continuous
Exercise 1.12.26
(Solution on p. 56.)
The sampling method was:
A. simple random
B. systematic
C. stratified
D. cluster
Exercise 1.12.27
(Solution on p. 56.)
“‘Duration (amount of time)”’ is what type of data?
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49
A. qualitative
B. quantitative - discrete
C. quantitative - continuous
Exercises 28 and 29 are not multiple choice exercises.
Exercise 1.12.28
(Solution on p. 56.)
Name the sampling method used in each of the following situations:
A. A woman in the airport is handing out questionnaires to travelers asking them to evaluate the
airport’s service. She does not ask travelers who are hurrying through the airport with their
hands full of luggage, but instead asks all travelers sitting near gates and who are not taking
naps while they wait.
B. A teacher wants to know if her students are doing homework so she randomly selects rows 2
and 5, and then calls on all students in row 2 and all students in row 5 to present the solution
to homework problems to the class.
C. The marketing manager for an electronics chain store wants information about the ages of its
customers. Over the next two weeks, at each store location, 100 randomly selected customers
are given questionnaires to fill out which asks for information about age, as well as about
other variables of interest.
D. The librarian at a public library wants to determine what proportion of the library users are
children. The librarian has a tally sheet on which she marks whether the books are checked
out by an adult or a child. She records this data for every 4th patron who checks out books.
E. A political party wants to know the reaction of voters to a debate between the candidates. The
day after the debate, the party’s polling staff calls 1200 randomly selected phone numbers.
If a registered voter answers the phone or is available to come to the phone, that registered
voter is asked who he/she intends to vote for and whether the debate changed his/her
opinion of the candidates.
** Contributed by Roberta Bloom
Exercise 1.12.29
(Solution on p. 57.)
Several online textbook retailers advertise that they have lower prices than on-campus book-
stores. However, an important factor is whether the internet retailers actually have the textbooks
that students need in stock. Students need to be able to get textbooks promptly at the beginning of
the college term. If the book is not available, then a student would not be able to get the textbook
at all, or might get a delayed delivery if the book is back ordered.
A college newspaper reporter is investigating textbook availability at online retailers.
He
decides to investigate one textbook for each of the following 7 subjects: calculus, biology,
chemistry, physics, statistics, geology, and general engineering. He consults textbook industry
sales data and selects the most popular nationally used textbook in each of these subjects. He
visits websites for a random sample of major online textbook sellers and looks up each of these 7
textbooks to see if they are available in stock for quick delivery through these retailers. Based on
his investigation, he writes an article in which he draws conclusions about the overall availability
of all college textbooks through online textbook retailers.
Write an analysis of his study that addresses the following issues: Is his sample representa-
tive of the population of all college textbooks? Explain why or why not. Describe some possible
sources of bias in this study, and how it might affect the results of the study. Give some sugges-
tions about what could be done to improve the study.
** Contributed by Roberta Bloom
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CHAPTER 1. SAMPLING AND DATA
1.13 Lab 1: Data Collection14
Class Time:
Names:
1.13.1 Student Learning Outcomes
• The student will demonstrate the systematic sampling technique.
• The student will construct Relative Frequency Tables.
• The student will interpret results and their differences from different data groupings.
1.13.2 Movie Survey
Ask five classmates from a different class how many movies they saw last month at the theater. Do not
include rented movies.
1. Record the data
2. In class, randomly pick one person. On the class list, mark that person’s name. Move down four
people’s names on the class list. Mark that person’s name. Continue doing this until you have marked
12 people’s names. You may need to go back to the start of the list. For each marked name record
below the five data values. You now have a total of 60 data values.
3. For each name marked, record the data:
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