CHAPTER
Introduction to Statistics
1
1.1 AN OVERVIEW OF STATISTICS
1.1 Try It Yourself Solutions
1a. The population consists of the prices per gallon of regular gasoline at all gasoline stations in the
United States. The sample consists of the prices per gallon of regular gasoline at the 900 surveyed
1.1 EXERCISE SOLUTIONS
1. A sample is a subset of a population.
2. It is usually impractical (too expensive and time consuming) to obtain all the population data.
3. A parameter is a numerical description of a population characteristic. A statistic is a numerical
description of a sample characteristic.
4. Descriptive statistics and inferential statistics
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11. The data set is a population because it is a collection of the heights of all the players on a school’s
basketball team.
14. The data set is a population because it is a collection of the annual salaries of all pharmacists at a
pharmacy.
15. Sample, because the collection of the 20 patients is a subset within the population
16. The data set is a population since it is a collection of the number of televisions in all U.S.
households.
20. Sample, because the collection of the 10 soil contamination levels is a subset in the population
21. Population: Party of registered voters in Warren County
Sample: Party of Warren County voters responding to online survey
24. Population: Income of all homeowners in Texas
Sample: Income of homeowners in Texas with mortgages
25. Population: Collection of all adults in the United States
Sample: Collection of 1000 adults surveyed
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29. Population: Collection of all registered voters
Sample: Collection of 800 registered voters surveyed
30. Population: Collection of all students at a college
Sample: Collection of 496 students surveyed
33. Population: Collection of all Fortune magazine’s top 100 companies to work for
Sample: Collection of the 85 companies who responded to the questionnaire
34. Population: Collection of all light bulbs from the day’s production
Sample: Collection of the 20 light bulbs selected from the day’s production
38. Parameter. 52% is a numerical description of the total number of governors.
39. Statistic. 8% is a numerical description of a sample of computer users.
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43. The statement “56% are the primary investors in their household” is an application of descriptive
statistics.
An inference drawn from the sample is that an association exists between U.S. women and being
the primary investor in their household.
45. Answers will vary.
46. (a) The volunteers in the study represent the sample.
(b) The population is the collection of all individuals who completed the math test.
47. (a) An inference drawn from the sample is that senior citizens who live in Florida have better
memory than senior citizens who do not live in Florida.
(b) It implies that if you live in Florida, you will have better memory.
48. (a) An inference drawn from the sample is that the obesity rate among boys ages 2 to 19 is
increasing.
1.2 DATA CLASSIFICATION
1.2 Try It Yourself Solutions
1a. One data set contains names of cities and the other contains city populations.
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2a. (1) The final standings represent a ranking of basketball teams.
(2) The collection of phone numbers represents labels. No mathematical computations can be
made.
b. (1) Interval, because the data can be ordered and meaningful differences can be calculated, but it
does not make sense writing a ratio using the temperatures
(2) Ratio, because the data can be ordered, can be written as a ratio, you can calculate
meaningful differences, and the data set contains an inherent zero
1.2 EXERCISE SOLUTIONS
1. Nominal and ordinal
4. False. For data at the interval level, you can calculate meaningful differences between data
entries. You cannot calculate meaningful differences at the nominal or ordinal level.
5. False. More types of calculations can be performed with data at the interval level than with data at
the nominal level.
9. Quantitative, because the body temperatures of patients is a numerical measure.
10. Qualitative, because the eye colors are merely labels
11. Quantitative, because the lengths of songs on an MP3 player are numerical measures
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18. Quantitative, because wait times at a grocery store are a numerical measure
19. Qualitative. Ordinal. Data can be arranged in order, but differences between data entries make no
sense.
22. Quantitative. Ratio. A ratio of two data values can be formed so one data value can be expressed
as a multiple of another.
25. Ordinal
26. Ratio
27. Nominal
28. Ratio
1.3 DATA COLLECTION AND EXPERIMENTAL DESIGN
1.3 Try It Yourself Solutions
1a. (1) Focus: Effect of exercise on relieving depression
(2) Focus: Success of graduates
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b. (1) Population: Collection of all people with depression
(2) Population: Collection of all university graduates at this large university
2a. There is no way to tell why people quit smoking. They could have quit smoking either from the
gum or from watching the DVD.
b. Two experiments could be done; one using the gum and the other using the DVD.
4a. (1) The sample was selected by only using the students in a randomly chosen class. Cluster
sampling
(2) The sample may be biased if there is any regularly occurring pattern in the data.
1.3 EXERCISE SOLUTIONS
1. In an experiment, a treatment is applied to part of a population and responses are observed. In an
observational study, a researcher measures characteristics of interest of part of a population but
does not change existing conditions.
4. Replication is the repetition of an experiment using a large group of subjects. It is important
because it gives validity to the results.
6. False. A double-blind experiment is used to decrease the placebo effect.
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7. False. Using stratified sampling guarantees that members of each group within a population will
be sampled.
10. True
11. Use a census because all the patients are accessible and the number of patients is not too large.
12. Perform an observational study because you want to observe and record motorcycle helmet usage.
15. Because it is impractical to create this situation, you would want to use a simulation.
16. Perform an observational study because you want to observe and record how often people wash
their hands in public restrooms.
17. (a) The experimental units are the 30–35 year old females being given the treatment. One
treatment is used.
18. (a) The experimental units are the 80 people with early signs of arthritis. One treatment is used.
(b) A problem with the design is that the sample size is small. The experiment could be
19. Each U.S. telephone number has an equal chance of being dialed and all samples of 1400 phone
numbers have an equal chance of being selected, so this is a simple random sample. Telephone
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20. Because the persons are divided into strata (rural and urban), and a sample is selected from each
stratum, this is a stratified sample.
21. Because the students were chosen due to their convenience of location (leaving the library), this is
22. Because the disaster area was divided into grids and thirty grids were then entirely selected, this
is a cluster sample. Certain grids may have been much more severely damaged than others, so this
is a possible source of bias.
24. Systematic sampling is used because every tenth person entering the shopping mall is sampled. It
is possible for bias to enter the sample if, for some reason, there is a regular pattern to people
entering the shopping mall.
26. Each telephone has an equal chance of being dialed and all samples of 1012 phone numbers have
an equal chance of being selected, so this is a simple random sample. Telephone sampling only
samples those individuals who have telephones and are willing to respond, so this is a possible
source of bias.
27. Answers will vary.
31. Census, because it is relatively easy to obtain the ages of the 115 residents
32. Sampling, because the population of subscribers is too large to easily record their favorite movie
type. Random sampling would be advised since it would be too easy to randomly select
subscribers then record their favorite movie type.
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36. Question is biased because it already suggests that the media has a negative effect on teen girls’
dieting habits. The question might be rewritten as “Do you think the media has an effect on teen
girls’ dieting habits?”
38. Stratified sampling ensures that each segment of the population is represented.
(a) Answers will vary.
39. Observational studies may be referred to as natural experiments because they involve observing
naturally occurring events that are not influenced by the study.
40. Open Question
Advantage: Allows respondent to express some depth and shades of meaning in the answer
Disadvantage: Not easily quantified and difficult to compare surveys
41. (a) Advantage: Usually results in a savings in the survey cost
(b) Disadvantage: There tends to be a lower response rate and this can introduce a bias into the
sample.
Sampling Technique: Convenience sampling
42. Answers will vary.
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CHAPTER 1 REVIEW EXERCISE SOLUTIONS
2. Population: Collection of all nurses in San Francisco area
Sample: Collection of 38 nurses in San Francisco area that were sampled
4. Population: Collection of all physicians in the U.S.
Sample: Collection of 1205 physicians that were sampled
8. Since 50% is describing a characteristic of a sample of U.S. adults who say they oppose drilling
for oil and gas in the Arctic National Wildlife Refuge, this is a statistic.
9. The average APR of 12.83% charged by credit cards is representative of the descriptive branch of
statistics. An inference drawn from the sample is that all credit cards charge an APR of 12.83%.
11. Quantitative, because monthly salaries are numerical measurements
12. Qualitative, because Social Security numbers are merely labels for employees
13. Quantitative, because ages are numerical measurements
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18. Ordinal. The data are qualitative but could be arranged in order of severity.
21. Because CEOs keep accurate records of charitable donations, you could take a census.
22. Because it is impractical to create this situation, you would want to perform a simulation.
25. The subjects could be split into male and female and then be randomly assigned to each of the
five treatment groups.
26. Number the volunteers and then use a random number generator to assign subjects to one of the
treatment groups or the control group.
27. Answers will vary.
30. Because the student sampled a convenient group of friends, this is a convenience sample.
31. Because each community is considered a cluster and every pregnant woman in a selected
community is surveyed, this is a cluster sample.
35. Telephone sampling only samples individuals who have telephones, are available, and are willing
to respond.
36. Due to the convenience sample taken, the study may be biased toward the opinions of the
student’s friends.
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38. It may be difficult for the law enforcement official to stop every third car.
CHAPTER 1 QUIZ SOLUTIONS
1. Population: Collection of all men
Sample: Collection of 20,000 men in study
4. (a) Ordinal. Badge numbers may be ordered numerically according to seniority of service, but no
mathematical computations can be made.
(b) Ratio. It makes sense to say that the horsepower of one car was twice as many as another car.
(c) Ordinal, because data can be arranged in order but the differences between data entries make
no sense
(d) Interval, because meaningful differences between entries can be calculated, but a zero entry is
not an inherent zero.
6. Randomized Block Design
7. (a) Because people were chosen due to their convenience of location (on the campground), this is
a convenience sample.
(b) Because every tenth part is selected from an assembly line, this is a systematic sample.