AP Statistics
Chapter 5 Review Questions
Name ______________________________
Is the right hand generally stronger than the left in right-handed
people? You can crudely measure hand strength by placing a bathroom
scale on a shelf with the end protruding and then squeezing the scale
between the thumb below and the four fingers above. The reading of the
scale shows the force exerted.
1. What is/are the explanatory variable(s)?
2. What is the response variable?
3. You have recruited 10 right-handed people to serve as subjects. In paragraph or algorithm form,
carefully describe the design of a matched-pairs experiment to compare the strength of the right and
left hands, using these subjects.
4. Start at line 139 in the Random Digit Table to do the required randomization and report your results.
139
140
80377
49106
66938
74818
59245
81250
81073
59894
58861
52924
35909 93654
79860 46942
34971
54238
5. During the 2000 presidential campaign, the candidates debated what to do with the large government
surplus. (Hard to imagine now, isn’t it?) The Pew Research Center asked two questions of random
samples of adults. Both questions stated that Social Security would be "fixed." Here are the uses
suggested for the remaining surplus:
a. Should the money be used for a tax cut, or should it be used to fund new government programs?
b. Should the money be used for a tax cut, or should it be spent on programs for education, the
environment, healthcare, crime-fighting and military defense?
One of these questions drew 60% favoring a tax cut; the other, only 22%. Which wording pulls
respondents toward a tax cut? Why?
6. There is an association between how well people do in school and how good they feel about
themselves. Perhaps helping people feel good about themselves will help them do better in school
and life. Raising self-esteem became for a time a goal in many schools. California even created a
state commission to advance the cause. Can you think of explanations for the association between
high self-esteem and good school performance other than "Self-esteem causes better work in school?"
A maker of fabric for clothing is setting up a new line to "finish" the raw fabric. The line will use either
metal rollers or natural-bristle rollers to raise the surface of the fabric; a dyeing-cycle time of either 30
or 40 minutes; and a temperature of either 150° or 175°C. An experiment will compare all combinations
of these choices. Three specimens of fabric will be subjected to each treatment and scored for quality.
7. What are the factors and treatments?
8. How many individuals (fabric specimens) does the experiment require?
A chemical engineer is designing the production process for a new product. The chemical reaction that
produces the product may have a higher or lower yield depending on the temperature and the stirring
rate in the vessel in which the reaction takes place. The engineer decides to investigate the effects of
combinations of two temperatures (50˚C and 60˚C) and three stirring rates (60 rpm, 90 rpm, and 120
rpm) on the yield of the process. Ten batches of feedstock will be processed at each combination of
temperature and stirring rate.
9. What are the experimental units?
(a)
(b)
(c)
(d)
(e)
The two temperatures (50˚C and 60˚C)
The three stirring rates (60 rpm, 90 rpm, and 120 rpm)
The two temperatures and the three stirring rates
The batches of feedstock
None of the above.
10. Identify all factors (explanatory variables).
(a)
(b)
(c)
(d)
(e)
The two temperatures (50˚C and 60˚C)
The three stirring rates (60 rpm, 90 rpm, and 120 rpm)
The two temperatures and the three stirring rates
The batches of feedstock
None of the above.
11. What is the response variable?
(a)
(b)
(c)
(d)
(e)
The two temperatures (50˚C and 60˚C)
The three stirring rates (60 rpm, 90 rpm, and 120 rpm)
The two temperatures and the three stirring rates
The batches of feedstock
None of the above.
12. How many treatments are there?
(a) 2
(b) 3
(c) 5
(d) 6
(e) None of the previous choices.
(d) 6
(e) None of the previous choices.
13. How many experimental units are needed?
(a) 2
(b) 3
(c) 5
14. You are doing a research project on attitudes toward fast food and decide to use as your sample the
first 25 people to enter the door at the local FatBurgers restaurant. Which of the following is true of
this sample?
(a) It is a systematic sample.
(c) It is a random sample.
(e) It is a self-selected sample.
(b) It is a convenience sample.
(d) It is a simple random sample
15. A double-blind design is important in an experiment because
(a) There is a natural tendency for subjects in an experiment to want to please the researcher.
(b) It helps control for the placebo effect.
(c) Evaluators of the responses in a study can influence the outcomes if they know which subjects
are in the treatment group and which are in the control group.
(d) Subjects in a study might react differently if they knew they were receiving an active treatment
or a placebo.
(e) All of the above are reasons why an experiment should be double-blind.
16. Which of the following are important in designing an experiment?
I.
II.
III.
(a)
(b)
(c)
(d)
(e)
Control of all variables that might have an influence on the response variable.
Randomization of subjects to treatment groups.
Use a large number of subjects to control for small-sample variability.
I only
I and II only
II and III only
I, II, and III
II only
17. A researcher observes that, on average, the number of divorces in cities with major league baseball
teams is larger than in cities without major league baseball teams. The most plausible explanation
for this observed association is that
(a) The presence of a major league baseball team causes the number of divorces to rise (perhaps
husbands are spending too much time at the ballpark).
(b) The high number of divorces is responsible for the presence of a major league baseball team
(more single people means potentially more fans at the ballpark, making it attractive for an
owner to relocate to such cities.)
(c) The association is due to common response (major league teams tend to be in large cities with
more people, thus a greater number of divorces.)
(d) The observed association is purely coincidental. It is impossible to believe the observed
association could be anything other than accidental.
18. Bias is present in the following sample design. Identify the type of bias involved and state whether
you think the sample proportion obtained is higher or lower than the true population proportion.
A political pollster is seeking information on public attitudes toward funding of pornographic art by
the National Endowment for the Arts (NEA). He asks a SRS of 2000 U. S. adults, “Rather than
support government censorship of artistic expression, are you in favor of continuing federal funding
of artists whose work may be controversial?” 85% of those surveyed answer “yes”.
Answers:
1. The explanatory variable is handedness
2. The response variable is the force exerted
3. • First, randomly select 5 people of the 10 people to use their left hand first and then the other 5 would use their right first.
This way I could control for the possibility that the first hand tried or the second hand tried may respond in a particular
way. (Perhaps the subject learns how to make the scale work the first time and then gives a better push the second, for
example.) Do this by numbering the people from 0 through 9 and then using a random number table or generator.
• Then, have each person push down on the scale with each hand and record the force exerted.
• Finally, find the difference between their two results. I would subtract (right – left) so that a positive value would mean
that the right hand was stronger than the left. (Since this is the way the question was worded.)
4. Number the people from 0 through 9. This is the most efficient because I only need single digits. Using line 139 I get: 5
8 9 4 and 0 in the first group. They will use their left hand first. The rest of them (1, 2, 3, 6, and 7) will use their right
hand first.
5. Question "a" will pull more people towards a tax cut. Most people would rather have the money than trust the government
to do "something" with it in some unnamed program. Question "b" names things most people would like to support, like
education and crime-fighting, so they are more likely to favor using money for those programs.
6. Instead of high self-esteem making people do well, doing well may make people feel good about themselves. The
causation may be the reverse of what the California group thinks.
7. Factors – type of roller, dyeing-cycle time and temperature
Treatments: (1) metal bristle, 30 minutes at 150°; (2) metal bristle, 30 minutes at 175°; (3) metal bristle, 40 minutes at
150°; (4) metal bristle, 40 minutes at 175°; (5) natural bristle, 30 minutes at 150°; (6) natural bristle, 40 minutes at 150°;
(7) natural bristle, 30 minutes at 175°; (8) natural bristle, 40 minutes at 175°.
8. 24. 9. d
10. c 11. e (it's the yield)
12. d
13. e (you need 60)
14. b. 15.e 16. d
17. c.
18. The wording of the question is poor. Reference to government censorship will result in more respondents in favor of the
other position (continuing federal funding for artists whose work is controversial.) The sample proportion is higher
than the population proportion.
Answers:
1. The explanatory variable is handedness
2. The response variable is the force exerted
3. • First, randomly select 5 people of the 10 people to use their left hand first and then the other 5 would use their right first.
This way I could control for the possibility that the first hand tried or the second hand tried may respond in a particular
way. (Perhaps the subject learns how to make the scale work the first time and then gives a better push the second, for
example.) Do this by numbering the people from 0 through 9 and then using a random number table or generator.
• Then, have each person push down on the scale with each hand and record the force exerted.
• Finally, find the difference between their two results. I would subtract (right – left) so that a positive value would mean
that the right hand was stronger than the left. (Since this is the way the question was worded.)
4. Number the people from 0 through 9. This is the most efficient because I only need single digits. Using line 139 I get: 5
8 9 4 and 0 in the first group. They will use their left hand first. The rest of them (1, 2, 3, 6, and 7) will use their right
hand first.
5. Question "a" will pull more people towards a tax cut. Most people would rather have the money than trust the government
to do "something" with it in some unnamed program. Question "b" names things most people would like to support, like
education and crime-fighting, so they are more likely to favor using money for those programs.
6. Instead of high self-esteem making people do well, doing well may make people feel good about themselves. The
causation may be the reverse of what the California group thinks.
7. Factors – type of roller, dyeing-cycle time and temperature
Treatments: (1) metal bristle, 30 minutes at 150°; (2) metal bristle, 30 minutes at 175°; (3) metal bristle, 40 minutes at
150°; (4) metal bristle, 40 minutes at 175°; (5) natural bristle, 30 minutes at 150°; (6) natural bristle, 40 minutes at 150°;
(7) natural bristle, 30 minutes at 175°; (8) natural bristle, 40 minutes at 175°.
8. 24. 9. d
10. c 11. e (it's the yield)
12. d
13. e (you need 60)
14. b. 15.e 16. d
17. c.
18. The wording of the question is poor. Reference to government censorship will result in more respondents in favor of the
other position (continuing federal funding for artists whose work is controversial.) The sample proportion is higher
than the population proportion.