SOLUTIONS MANUAL
JAMES LAPP
Colorado Mesa University
ELEMENTARY STATISTICS
USING THE TI-83/84 PLUS CALCULATOR
FIFTH EDITION
Mario F. Triola

CONTENTS
Chapter 1: Introduction To Statistics
Section 1-1: Statistical and Critical Thinking ...................................................................1
Section 1-2: Types of Data ...............................................................................................3
Section 1-3: Collecting Sample Data ................................................................................4
Section 1-4: Introduction to the TI-83/84 Plus Calculator................................................5
Chapter Quick Quiz ..........................................................................................................7
Review Exercises ..............................................................................................................7
Cumulative Review Exercises ..........................................................................................8
Chapter 2: Exploring Data with Tables and Graphs
Section 2-1: Frequency Distributions for Organizing and Summarizing Data ...............11
Section 2-2: Histograms ..................................................................................................16
Section 2-3: Graphs That Enlighten and Graphs That Deceive ......................................18
Section 2-4: Scatterplots, Correlation, and Regression ..................................................22
Chapter Quick Quiz ........................................................................................................24
Review Exercises ............................................................................................................24
Cumulative Review Exercises ........................................................................................26
Chapter 3: Describing, Exploring, and Comparing Data
Section 3-1: Measures of Center .....................................................................................27
Section 3-2: Measures of Variation ................................................................................39
Section 3-3: Measures of Relative Standing and Boxplots .............................................49
Chapter Quick Quiz ........................................................................................................54
Review Exercises ............................................................................................................55
Cumulative Review Exercises ........................................................................................56
Chapter 4: Probability
Section 4-1: Basic Concepts of Probability ....................................................................59
Section 4-2: Addition Rule and Multiplication Rule ......................................................62
Section 4-3: Complements, Conditional Probability, and Bayes’ Theorem ...................65
Section 4-4: Counting .....................................................................................................68
Chapter Quick Quiz ........................................................................................................72
Review Exercises ............................................................................................................73
Cumulative Review Exercises ........................................................................................75
Chapter 5: Discrete Probability Distributions
Section 5-1: Probability Distributions ............................................................................79
Section 5-2: Binomial Probability Distributions.............................................................83
Section 5-3: Poisson Probability Distributions ...............................................................89
Chapter Quick Quiz ........................................................................................................92
Review Exercises ............................................................................................................93
Cumulative Review Exercises ........................................................................................95

Chapter 6: Normal Probability Distributions
Section 6-1: The Standard Normal Distribution .............................................................99
Section 6-2: Real Applications of Normal Distributions ..............................................103
Section 6-3: Sampling Distributions and Estimators ....................................................109
Section 6-4: The Central Limit Theorem ......................................................................117
Section 6-5: Assessing Normality .................................................................................122
Section 6-6: Normal as Approximation to Binomial ....................................................125
Chapter Quick Quiz ......................................................................................................130
Review Exercises ..........................................................................................................131
Cumulative Review Exercises ......................................................................................134
Chapter 7: Estimating Parameters and Determining Sample Sizes
Section 7-1: Estimating a Population Proportion..........................................................137
Section 7-2: Estimating a Population Mean..................................................................145
Section 7-3: Estimating a Population Standard Deviation or Variance ........................154
Section 7-4: Bootstrapping: Using Technology for Estimates .....................................159
Chapter Quick Quiz ......................................................................................................161
Review Exercises ..........................................................................................................162
Cumulative Review Exercises ......................................................................................164
Chapter 8: Hypothesis Testing
Section 8-1: Basics of Hypothesis Testing ...................................................................167
Section 8-2: Testing a Claim About a Proportion.........................................................169
Section 8-3: Testing a Claim About a Mean .................................................................182
Section 8-4: Testing a Claim About a Standard Deviation or Variance .......................189
Chapter Quick Quiz ......................................................................................................193
Review Exercises ..........................................................................................................194
Cumulative Review Exercises ......................................................................................196
Chapter 9: Chapter 9: Inferences from Two Samples
Section 9-1: Two Proportions .......................................................................................199
Section 9-2: Two Means: Independent Samples ...........................................................213
Section 9-3: Two Dependent Samples (Matched Pairs) ...............................................224
Section 9-4: Two Variances or Standard Deviations ....................................................232
Chapter Quick Quiz ......................................................................................................236
Review Exercises ..........................................................................................................236
Cumulative Review Exercises ......................................................................................239
Chapter 10: Correlation and Regression
Section 10-1: Correlation ..............................................................................................243
Section 10-2: Regression ..............................................................................................249
Section 10-3: Prediction Intervals and Variation ..........................................................266
Section 10-4: Multiple Regression................................................................................268
Section 10-5: Nonlinear Regression .............................................................................271
Chapter Quick Quiz ......................................................................................................276
Review Exercises ..........................................................................................................277
Cumulative Review Exercises ......................................................................................279

Chapter 11: Goodness-of-Fit and Contingency Tables
Section 11-1: Goodness-of-Fit ......................................................................................283
Section 11-2: Contingency Tables ................................................................................292
Chapter Quick Quiz ......................................................................................................299
Review Exercises ..........................................................................................................300
Cumulative Review Exercises ......................................................................................302
Chapter 12: Analysis of Variance
Section 12-1: One-Way ANOVA .................................................................................307
Section 12-2: Two-Way ANOVA ................................................................................310
Chapter Quick Quiz ......................................................................................................311
Review Exercises ..........................................................................................................311
Cumulative Review Exercises ......................................................................................312
Chapter 13: Nonparametric Tests
Section 13-1: Basics of Nonparametric Tests (Not available: no exercises)
Section 13-2: Sign Test .................................................................................................315
Section 13-3: Wilcoxon Signed-Ranks Test for Matched Pairs ...................................317
Section 13-4: Wilcoxon Rank-Sum Test for Two Independent samples ......................320
Section 13-5: Kruskal-Wallis Test for Three or More Samples ...................................325
Section 13-6: Rank Correlation ....................................................................................328
Section 13-7: Runs Test for Randomness .....................................................................330
Chapter Quick Quiz ......................................................................................................332
Review Exercises ..........................................................................................................332
Cumulative Review Exercises ......................................................................................335
Chapter 14: Statistical Process Control
Section 14-1: Control Charts for Variation and Mean ..................................................337
Section 14-2: Control Charts for Attributes ..................................................................339
Chapter Quick Quiz ......................................................................................................344
Review Exercises ..........................................................................................................345
Cumulative Review Exercises ......................................................................................346
Chapter 15: Ethics In Statistics
(Not available: no exercises)

Section 1-1: Statistical and Critical Thinking 1
Chapter 1: Introduction to Statistics
Section 1-1: Statistical and Critical Thinking
1. The respondents are a voluntary response sample or a self-selected sample. Because those with strong interests
in the topic are more likely to respond, it is very possible that their responses do not reflect the opinions or
behavior of the general population.
2. a. The sample consists of the 1046 adults who were surveyed. The population consists of all adults.
b. When asked, respondents might be inclined to avoid the shame of the unhealthy habit of not washing their
hands, so the reported rate of 70% might well be much higher than it is in reality. It is generally better to
observe or measure human behavior than to ask subjects about it.
3. Statistical significance is indicated when methods of statistics are used to reach a conclusion that a treatment is
effective, but common sense might suggest that the treatment does not make enough of a difference to justify its
use or to be practical. Yes, it is possible for a study to have statistical significance, but not practical
significance.
4. No. Correlation does not imply causation. The example illustrates a correlation that is clearly not the result of
any interaction or cause effect relationship between deaths in swimming pools and power generated from
nuclear power plants.
5. Yes, there does appear to be a potential to create a bias.
6. No, there does not appear to be a potential to create a bias.
7. No, there does not appear to be a potential to create a bias.
8. Yes, there does appear to be a potential to create a bias.
9. The sample is a voluntary response sample and has strong potential to be flawed.
10. The samples are voluntary response samples and have potential for being flawed, but this approach might be
necessary due to ethical considerations involved in randomly selecting subjects and somehow imposing
treatments on them.
11. The sampling method appears to be sound.
12. The sampling method appears to be sound.
13. With only a 1% chance of getting such results with a program that has no effect, the program appears to have
statistical significance. Also, because the average loss of 22 pounds does seem substantial, the program appears
to also have practical significance.
14. Because there is a 0.3% chance of getting such results by chance, the increase in scores does appear to have
statistical significance. The typical increase of 5 points suggests that the course does have practical significance.
The course does appear to be successful.
15. Because there is a 19% chance of getting that many girls by chance, the method appears to lack statistical
significance. The result of 1020 girls in 2000 births (51% girls) is above the approximately 50% rate expected
by chance, but it does not appear to be high enough to have practical significance. Not many couples would
bother with a procedure that raises the likelihood of a girl from 50% to 51%.
16. Because there is a 25% chance of getting such results with a program that has no effect, the program does not
appear to have statistical significance. Because the average increase is only 3 IQ points, the program does not
appear to have practical significance.
17. Yes. Each column of 8 AM and 12 AM temperatures is recorded from the same subject, so each pair is
matched.
18. No. The source is from university researchers who do not appear to gain from distorting the data.
19. The data can be used to address the issue of whether there is a correlation between body temperatures at
8 AM and at 12 AM. Also, the data can be used to determine whether there are differences between body
temperatures at 8 AM and at 12 AM.

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2 Chapter 1: Introduction to Statistics
20. Because the differences could easily occur by chance (with a 64% chance), the differences do not appear to
have statistical significance.
21. No. The white blood cell counts measure a different quantity than the red blood cell counts, so their differences
are meaningless.
22. The issue that can be addressed is whether there is a correlation, or association, between white blood cell counts
and red blood cell counts.
23. No. The National Center for Health Statistics has no reason to collect or present the data in a way that is biased.
24. No. Correlation does not imply causation, so a statistical correlation between white blood cell counts and red
blood cell counts should not be used to conclude that higher white blood cell counts are the cause of higher red
blood cell counts.
25. It is questionable that the sponsor is the Idaho Potato Commission and the favorite vegetable is potatoes.
26. The sample is a voluntary response sample, so there is a good chance that the results do not reflect the larger
population of people who have a water preference.
27. The correlation, or association, between two variables does not mean that one of the variables is the cause of the
other. Correlation does not imply causation. Clearly, sour cream consumption is not directly related in any way
to motorcycle fatalities.
28. The sponsor of the poll is an electronic cigarette maker, so the sponsor does have an interest in the poll results.
The source is questionable.
29. a. 700 adults
b. 55%
30. a. 253.31 subjects
b. No. Because the result is a count of people among the 347 who were surveyed, the result must be a whole
number.
c. 253 subjects
d. 32%
31. a. 559.2 respondents
b. No. Because the result is a count of respondents among the 1165 engaged or married women who were
surveyed, the result must be a whole number.
c. 559 respondents
d. 8%
32. a. 293.17 women
b. No. Because the result is a count of women among the 1543 who were surveyed, the result must be a whole
number.
c. 293 women
d. 15%
e. Interpretations of a “typical” week and what it means to “kick back and relax” might vary considerably by
different survey respondents. The survey might be improved by asking about behavior within “the past seven
days” instead of a “typical” week. Instead of “kick back and relax,” respondents might be surveyed about
specific behavior, such as reading, taking a nap, watching television, listening to music, or going for a walk.
33. Because a reduction of 100% would eliminate all of the size, it is not possible to reduce the size by 100% or
more.
34. In an editorial criticizing the statement, the New York Times correctly interpreted the 100% improvement to
mean that no baggage is being lost, which was not true.
35. Because a reduction of 100% would eliminate all plaque, it is not possible to reduce it by more than 100%.

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Section 1-2: Types of Data 3
36. If one subgroup receives a 4% raise and another subgroup receives a 4% raise, the combined group will receive
a 4% raise, not an 8% raise. The percentages should not be added in this case.
37. The wording of the question is biased and tends to encourage negative responses. The sample size of 20 is too
small. Survey respondents are self-selected instead of being randomly selected by the newspaper. If 20 readers
respond, the percentages should be multiples of 5, so 87% and 13% are not possible results.
38. All percentages of success should be multiples of 5. The given percentages cannot be correct.
Section 1-2: Types of Data
1. The population consists of all adults in the United States, and the sample is the 2276 adults who were surveyed.
Because the value of 33% refers to the sample, it is a statistic.
2. a. quantitative
b. categorical
c. categorical
d. quantitative
3. Only part (a) describes discrete data.
4. a. The sample is the 1020 adults who were surveyed. The population is all adults in the United States.
b. statistic
c. ratio
d. discrete
5. statistic
6. statistic
7. parameter
8. parameter
9. statistic
10. statistic
11. parameter
12. parameter
13. continuous
14. continuous
15. discrete
16. discrete
17. discrete
18. continuous
19. continuous
20. discrete
21. ordinal
22. nominal
23. nominal
24. ratio
25. interval
26. ordinal
27. ordinal
28. interval
29. The numbers are not counts or measures of anything. They are at the nominal level of measurement, and it
makes no sense to compute the average (mean) of them.
30. The digits are not counts or measures of anything. They are at the nominal level of measurement and it makes
no sense to calculate their average (mean).
31. The temperatures are at the interval level of measurement. Because there is no natural starting point with 0 F
representing “no heat,” ratios such as “twice” make no sense, so it is wrong to say that it is twice as warm at the
author’s home as it is in Auckland, New Zealand.
32. The ranks are at the ordinal level of measurement. Differences between the universities cannot be determined,
so there is no way to know whether the difference between Princeton and Harvard is the same as the difference
between Yale and Columbia.
33. a. Continuous, because the number of possible values is infinite and not countable.
b. Discrete, because the number of possible values is finite.
c. Discrete, because the number of possible values is finite.
d. Discrete, because the number of possible values is infinite and countable.

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4 Chapter 1: Introduction to Statistics
Section 1-3: Collecting Sample Data
1. The study is an experiment because subjects were given treatments.
2. The subjects in the study did not know whether they were taking a placebo or the paracetamol medication, and
those who administered the pills also did not know.
3. The group sample sizes of 547, 550, and 546 are all large so that the researchers could see the effects of the
paracetamol treatment.
4. The sample appears to be a convenience sample. Given that the subjects were randomly assigned to the three
different treatment groups, it appears that the results of the study are good because they are not likely to be
distorted from bias, but we should investigate the sample groups to ensure that they are not fundamentally
different from the population.
5. The sample appears to be a convenience sample. By e-mailing the survey to a readily available group of Internet
users, it was easy to obtain results. Although there is a real potential for getting a sample group that is not
representative of the population, indications of which ear is used for cell phone calls and which hand is
dominant do not appear to be factors that would be distorted much by a sample bias.
6. The study is an observational study because the subjects were not given any treatment.
7. With 717 responses, the response rate is 14%, which does appear to be quite low. In general, a very low
response rate creates a serious potential for getting a biased sample that consists of those with a special interest
in the topic.
8. Answers vary, but the following are good possibilities.
a. Obtain a printed copy of the class roster, assign consecutive numbers (integers), then use a computer to
randomly generate six of those numbers.
b. Select every third student leaving class until six students are chosen.
c. Randomly select three males and three females.
d. Randomly select a row, and then select the students in that row. (Use only the first six to meet the
requirement of a sample of size six.)
9. systematic
10. convenience
11. random
12. stratified
13. cluster
14. random
15. stratified
16. systematic
17. random
18. cluster
19. convenience
20. systematic
21. Observational study. The sample is a convenience sample consisting of subjects who decided themselves to
respond. Such voluntary response samples have a high chance of not being representative of the larger
population, so the sample may well be biased. The question was posted in an electronic edition of a newspaper,
so the sample is biased from the beginning.
22. Experiment. The sample subjects consist of male physicians only. It would have been better to include females.
Also, it would be better to include male and females who are not physicians.
23. Experiment. This experiment would create an extremely dangerous and illegal situation that has a real potential
to result in injury or death. It’s difficult enough to drive in New York City while being completely sober.
24. Observational study. The sample of four males and four females is too small.
25. Experiment. The biased sample created by using drivers from New York City cannot be fixed by using a larger
sample. The larger sample will still be a biased sample that is not representative of drivers in the United States.
26. Experiment. Calling the subjects and asking them to report their weights has a high risk of getting results that do
not reflect the actual weights. It would have been much better to somehow measure the weights instead of
asking the subjects to report them.

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Section 1-4: Introduction to the TI-83/84 Plus Calculator 5
27. Observational study. Respondents who have been convicted of felonies are not likely to respond honestly to the
second question. The survey will suffer from a “social desirability bias” because subjects will tend to respond in
ways that will be viewed favorably by those conducting the survey.
28. Observational study. The number of responses is very small, and the response rate of only 1.52% is far too
small. With such a low response rate, there is a real possibility that the sample of respondents is biased and
consists only of those with special interests in the survey topic.
29. prospective study
30. retrospective study
31. cross-sectional study
32. prospective study
33. matched pairs design
34. randomized block design
35. completely randomized design
36. matched pairs design
37. a. Not a simple random sample, but it is a random sample.
b. Simple random sample and also a random sample.
c. Not a simple random sample and not a random sample.
Section 1-4: Introduction to the TI-83/84 Plus Calculator
1. The [ key is used instead of the equals key.
2. The LIST menu is obtained, and it shows a top line of NAMES OPS MATH followed by the list names.
3. The c key is used for the operation of subtraction, and the : key is used for the negative sign.
4. In this context, “ALPHA” is a shortened version of “alphabetic” character or expression.
5. 90 6. 12
TI Output for Exercises 5 and 7 TI Output for Exercises 6 and 8
7. 27 8. 0.321
9. 10 10. 40
TI Output for Exercises 9 and 11 TI Output for Exercises 10 and 12
11. 2 12. 0.924491486213

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6 Chapter 1: Introduction to Statistics
13. 1024, which is 5
4 . 14. 16, which is 2
4 .
TI Output for Exercise 13 TI Output for Exercises 14 and 16
15. ERR: SYNTAX, which is a syntax error that occurs because : indicates a negative sign (not the operation of
subtraction).
16. 8, which is the value of 4 subtracted from 12.
17.  72 87 74 93 , which is a display of the original list of values.
18.  2 17 4 23 , which is a list of the original values after 70 has been subtracted from each value.
TI Output for Exercises 17 and 19 TI Output for Exercises 18 and 20
19.  5184 7569 5476 8649 , which is a list of the original values after each value has been squared.
20.  2 17 4 23 , which is a list of the original values after -70 has been added to each of them. (This is equivalent
to subtracting 70 from each value.)
21. 0.00003051757813 22. 30517578130
TI Output for Exercises 21 and 23 TI Output for Exercises 22 and 24
23. 1099511628000 24. 0.0000001024

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Chapter Quick Quiz 7
25. a. The result will vary, but it will probably not
be the list of values, because the symbol is
needed to designate ABC as a list.
b.  0 2 5 8 1 , which is the original list of
values.
c.  0 4 25 64 1 , which is a list of the squares
of the original values.
TI Output for Exercise 25
Chapter Quick Quiz
1. No. The numbers do not measure or count anything.
2. nominal
3. continuous
4. quantitative data
5. ratio
6. statistic
7. no
8. observational study
9. The subjects did not know whether they were getting aspirin or the placebo.
10. simple random sample
Review Exercises
1. The survey sponsor has the potential to gain from the results, which raises doubts about the objectivity of the
results.
2. a. The sample is a voluntary response sample, so the results are questionable.
b. statistic
c. observational study
3. Randomized: Subjects were assigned to the different groups through a process of random selection, whereby
they had the same chance of belonging to each group. Double-blind: The subjects did not know which of the
three groups they were in, and the people who evaluated results did not know either.
4. No. Correlation does not imply causality. 5. Only part (c) is a simple random sample.
6. Yes. The two questions give the false impression that they are addressing very different issues. Most people
would be in favor of defending marriage, so the first question is likely to receive a substantial number of “yes”
responses. The second question better describes the issue and subjects are much more likely to have varied
responses.
7. a. discrete
b. ratio
c. The mailed responses would be a voluntary response sample, so those with strong opinions or greater interest
in the topics are more likely to respond. It is very possible that the results do not reflect the true opinions of the
population of all full-time college students.
d. stratified
e. cluster
8. a. If they have no fat at all, they have 100% less than any other amount with fat, so the 125% figure cannot be
correct.
b. 686
c. 28%

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8 Chapter 1: Introduction to Statistics
9. a. interval data; systematic sample
b. nominal data; stratified sample
c. ordinal data; convenience sample
10. Because there is a 15% chance of getting the results by chance, those results could easily occur by chance so the
method does not appear to have statistical significance. The result of 236 girls in 450 births is a rate of 52.4%,
so it is above the 50% rate expected by chance, but it does not appear to be high enough to have practical
significance. The procedure does not appear to have either statistical significance or practical significance.
Cumulative Review Exercises
1. The mean is 3600 1700 4000 3900 3100 3800 2200 3000 3162.5
8
        grams. The weights all end with
00, suggesting that all of the weights are rounded to the hundreds place, so that the last two digits are always 00.
2. 6
0.5 0.015625
TI Output for Exercises 1 and 3 TI Output for Exercises 2 and 4
3. 272 176 16;
6
  This is an unusually high value. 4. 98.2 98.6 6.64
0.62
106
  
5.
2
2
1.96 0.25 1067
0.03
  6. 4000 1700 575
4
  grams
TI Output for Exercises 5 and 7 TI Output for Exercises 6 and 8
7.  2
3600 3162.5 27, 343.75
7
  grams2
8.      2 2 2
98.4 98.6 98.6 98.6 98.8 98.6 0.04 0.20
3 1
      


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Section 2-1: Frequency Distributions for Organizing and Summarizing Data 11
Chapter 2: Exploring Data with Tables and Graphs
Section 2-1: Frequency Distributions for Organizing and Summarizing Data
1. The table summarizes 50 service times. It is not possible to identify the exact values of all of the original times.
2. The classes of 60–120, 120–180, …, 300–360 overlap, so it is not always clear which class we should put a
value in. For example, the value of 120 could go in the first class or the second class. The classes should be
mutually exclusive.
3.
Time (sec) Relative Frequency
60–119 14%
120–179 44%
180–239 28%
240–299 4%
300–359 10%
4. The sum of the relative frequencies is 125%, but it should be 100%, with a small round off error. All of the
relative frequencies appear to be roughly the same, but if they are from a normal distribution, they should start
low, reach a maximum, and then decrease.
5. Class width: 10
Class midpoints: 24.5, 34.5, 44.5, 54.5, 64.5, 74.5, 84.5
Class boundaries: 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5, 89.5
Number: 87
6. Class width: 10
Class midpoints: 24.5, 34.5, 44.5, 54.5, 64.5, 74.5
Class boundaries: 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5
Number: 87
7. Class width: 100
Class midpoints: 49.5, 149.5, 249.5, 349.5, 449.5, 549.5, 649.5
Class boundaries: –0.5, 99.5, 199.5, 299.5, 399.5, 499.5, 599.5, 699.5
Number: 153
8. Class width: 100
Class midpoints: 149.5, 249.5, 349.5, 449.5, 549.5
Class boundaries: 99.5, 199.5, 299.5, 399.5, 499.5, 599.5
Number: 147
9. No. The maximum frequency is in the second class instead of being near the middle, so the frequencies below
the maximum do not mirror those above the maximum.
10. Yes. The frequencies start low, reach a maximum of 36, and then decrease. The values below the maximum are
very roughly a mirror image of those above it.
11.
Duration (sec) Frequency
125–149 1
150–174 0
175–199 0
200–224 3
225–249 34
250–274 12
TI Output for Exercise 11
[125, 275] by [0, 36]

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