Frequency
Relative Frequency
Cumulative
Relative
Frequency
1
30
0.6
2
15
3
Table 1.10
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 1.11.3
(Solution on p. 42.)
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
11This content is available online at <http://cnx.org/content/m16010/1.17/>.
30
CHAPTER 1. SAMPLING AND DATA
Table 1.11
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 1.11.4
A fitness center is interested in the average 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 1.11.5
(Solution on p. 42.)
Ski resorts are interested in the average 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 1.11.6
A cardiologist is interested in the average 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 1.11.7
(Solution on p. 42.)
Insurance companies are interested in the average 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
31
Exercise 1.11.8
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 1.11.9
(Solution on p. 43.)
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 1.11.10
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 1.11.11
(Solution on p. 43.)
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 1.11.12
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.
32
CHAPTER 1. SAMPLING AND DATA
Exercise 1.11.13
Suppose you want to determine the average number of students per statistics class in your state.
Describe a possible sampling method in 3 – 5 complete sentences. Make the description detailed.
Exercise 1.11.14
Suppose you want to determine the average 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 1.11.15
726 distance learning students at Long Beach City College in the 2004-2005 academic year were
surveyed and asked the reasons they took a distance learning class. (Source: Amit Schitai, Director
of Instructional Technology and Distance Learning, LBCC ). The results of this survey are listed in
the table below.
Reasons for Taking LBCC Distance Learning Courses
Convenience
87.6%
Unable to come to campus
85.1%
Taking on-campus courses in addition to my DL course
71.7%
Instructor has a good reputation
69.1%
To fulfill requirements for transfer
60.8%
To fulfill requirements for Associate Degree
53.6%
Thought DE would be more varied and interesting
53.2%
I like computer technology
52.1%
Had success with previous DL course
52.0%
On-campus sections were full
42.1%
To fulfill requirements for vocational certification
27.1%
Because of disability
20.5%
Table 1.12
Assume that the survey allowed students to choose from the responses listed in the table above.
a. Why can the percents add up to over 100%?
b. Does that necessarily imply a mistake in the report?
c. How do you think the question was worded to get responses that totaled over 100%?
d. How might the question be worded to get responses that totaled 100%?
Exercise 1.11.16
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:
33
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 1.13
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 1.11.17
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 1.11.18
34
CHAPTER 1. SAMPLING AND DATA
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.
1.11.1 Try these multiple choice questions
The next four questions refer to the following: A Lake Tahoe Community College instructor is interested
in the average number of days Lake Tahoe Community College math students are absent from class during
a quarter.
Exercise 1.11.19
(Solution on p. 43.)
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 1.11.20
(Solution on p. 43.)
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 1.11.21
(Solution on p. 43.)
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 1.11.22
(Solution on p. 43.)
The instructor’s sample produces an average 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 12)
12http://www.nhc.noaa.gov/gifs/table5.gif
35
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 1.14
Exercise 1.11.23
(Solution on p. 43.)
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 1.11.24
(Solution on p. 43.)
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 1.11.25
(Solution on p. 43.)
“‘Number of times per week”’ is what type of data?
A. qualitative
B. quantitative - discrete
C. quantitative - continuous
Exercise 1.11.26
(Solution on p. 43.)
The sampling method was:
A. simple random
B. systematic
C. stratified
D. cluster
Exercise 1.11.27
(Solution on p. 43.)
“‘Duration (amount of time)”’ is what type of data?
36
CHAPTER 1. SAMPLING AND DATA
A. qualitative
B. quantitative - discrete
C. quantitative - continuous
Exercise 1.11.28
(Solution on p. 43.)
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 1.11.29
(Solution on p. 43.)
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
37
1.12 Lab 1: Data Collection13
Class Time:
Names:
1.12.1 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.
1.12.2 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:
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
______
Table 1.15
1.12.3 Order the Data
Complete the two relative frequency tables below using your class data.
13This content is available online at <http://cnx.org/content