SOLUTIONS for
Elementary Statistics Using the TI-
83/84 Plus Calculator, 4th edition
ST
Author (s): Mario F. Triola
UV
IA
_A
PP
RO
VE
D?
, Chapter 1: Introduction to Statistics 1
Chapter 1: Introduction to Statistics
Section 1-2 Statistical and Critical Thinking
1. Statistical significance is indicated when methods of statistics are used to reach a conclusion that some
treatment or finding is effective, but common sense might suggest that the treatment or finding 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 a practical significance.
2. If the source of the data can benefit from the results of the study, it is possible that an element of bias is
ST
introduced so that the results are favorable to the source.
3. A voluntary response sample is a sample in which the subjects themselves decide whether to be included in
the study. A voluntary response sample is generally not suitable for a statistical study because the sample
may have a bias resulting from participation by those with a special interest in the topic being studied.
UV
4. Even if we conduct a study and find that there is a correlation, or association, between two variables, we
cannot conclude that one of the variables is the cause of the other.
5. There does appear to be a potential to create a bias.
6. There does not appear to be a potential to create a bias.
IA
7. There does not appear to be a potential to create a bias.
8. There does appear a potential to create a bias.
9. The sample is a voluntary response sample and is therefore flawed.
_A
10. The sample is a voluntary response sample and is therefore flawed.
11. The sampling method appears to be sound.
12. The sampling method appears to be sound.
PP
13. Because there is a 30% chance of getting such results with a diet that has no effect, it does not appear to
have statistical significance, but the average loss of 45 pounds does appear to have practical significance.
14. Because there is only a 1% chance of getting the results by chance, the method appears to have a statistical
significance. The result of 540 boys in 1000 births 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
RO
bother with a procedure that raises the likelihood of a boy from 50% to 54%.
15. Because there is a 23% chance of getting such results with a program that has no effect, the program does
not appear to have statistical significance. Because the success rate of 23% is not much better than the 20%
rate that is typically expected with random guessing, the program does not appear to have practical
significance.
VE
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 point, the program
does not appear to have practical significance.
17. The male and female pulse rates in the same column are not matched in any meaningful way. It does not
make sense to use the difference between any of the pulse rates that are in the same column.
D?
18. Yes, the source of the data is likely to be unbiased.
19. The data can be used to address the issue of whether males and females have pulse rates with the same
average (mean) value.
20. The results do not prove that the populations of males and females have the same average (mean) pulse
rate. The results are based on a particular sample of five males and five females, and analyzing other
samples might lead to a different conclusion. Better results would be obtained with larger samples.
Copyright © 2015 Pearson Education, Inc.
,2 Elementary Statistics Using the TI-83/84 Plus Calculator, 4th edition
21. Yes, each IQ score is matched with the brain volume in the same column, because they are measurements
obtained from the same person. It does not make sense to use the difference between each IQ score and the
brain volume in the same column, because IQ scores and brain volumes use different units of measurement.
For example, it would make no sense to find the difference between an IQ score of 87 and a brain volume
of 1035 cm3.
22. The issue that can be addressed is whether there is a correlation, or association, between IQ score and brain
volume.
23. Given that the researchers do not appear to benefit from the results, they are professionals at prestigious
ST
institutions, and funding is from a U.S. government agency, the source of the data appears to be unbiased.
24. No. Correlation does not imply causation, so a statistical correlation between IQ score and brain volume
should not be used to conclude that larger brain volumes cause higher IQ scores.
25. It is questionable that the sponsor is the Idaho Potato Commission and the favorite vegetable is potatoes.
UV
26. The sample is a voluntary response sample, so there is a good chance that the results are not valid.
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.
28. The correlation, or association, between two variables does not mean that one of the variables is the cause
IA
of the other. Correlation does not imply causation.
29. a. The number of people is (0.39)(1018) = 397.02
b. No. Because the result is a count of people among 1018 who were surveyed, the result must be a whole
_A
number.
c. The actual number is 397 people
255
d. The percentage is = 0.25049 = 25%
1018
PP
30. a. The number of women is (0.38)(427) = 162.26
b. No. Because the result is a count of women among 427 who were surveyed, the result must be a whole
number.
b. The actual number is 162 women.
RO
30
d. The percentage is = 0.07026 = 7%
427
31. a. The number of adults is (0.14)(2302) = 322.28
b. No. Because the result is a count of adults among 2302 who were surveyed, the result must be a whole
number.
VE
c. The actual number is 322 adults.
46
d. The percentage is = 0.01998 = 2%
2302
32. a. The number of adults is (0.76)(2513) = 1909.88
D?
b. No. Because the result is a count of adults among 2513 who were surveyed, the result must be a whole
number.
b. The actual number is 1910 adults.
327
d. The percentage is = 0.13012 = 13%
2513
33. Because a reduction of 100% would eliminate all of the size, it is not possible to reduce the size by 100%
or more.
Copyright © 2015 Pearson Education, Inc.
, Chapter 1: Introduction to Statistics 3
34. If the Club eliminated all car thefts, it would reduce the odds of car theft by 100%, so the 400% figure is
impossible.
35. If foreign investment fell by 100% it would be totally eliminated, so it is not possible for it to fall by more
than 100%.
36. Because a reduction of 100% would eliminate all plague, it is not possible to reduce it by more than 100%.
37. Without our knowing anything about the number of ATVs in use, or the number of ATV drivers, or the
amount of ATV usage, the number of 740 fatal accidents has no context. Some information should be
ST
given so that the reader can understand the rate of ATV fatalities.
38. All percentages of success should be multiples of 5. The given percentage cannot be correct.
39. The wording of the question is biased and tends to encourage negative response. The sample size of 20 is
too small. Survey respondents are self-selected instead of being selected by the newspaper. If 20 readers
UV
respond, the percentages should be multiples of 5, so 87% and 13% are not possible results.
Section 1-3 Types of Data
1. A parameter is a numerical measurement describing some characteristic of a population, whereas a statistic
is a numerical measurement describing some characteristic of a sample.
IA
2. Quantitative data consist of numbers representing counts or measurements, whereas categorical data can be
separated into different categories that are distinguished by some characteristic that is not numerical.
3. Parts (a) and (c) describe discrete data.
4. The values of 1010 and 55% are both statistics because they are based on the sample. The population
_A
consists of all adults in the United States.
5. Statistic 17. Discrete
6. Parameter 18. Discrete
7. Parameter 19. Continuous
PP
8. Statistic 20. Continuous
9. Parameter 21. Nominal
10. Parameter 22. Ratio
RO
11. Statistic 23. Interval
12. Statistic 24. Ordinal
13. Continuous 25. Ratio
14. Discrete 26. Nominal
VE
15. Discrete 27. Ordinal
16. Continuous 28. Interval
29. The numbers are not counts or measures of anything, so they are at the nominal level of measurement, and
it makes no sense to compute the average (mean) of them.
D?
30. The flight numbers do not count or measure anything. They are at the nominal level of measurement, and it
does not make sense to compute the average (mean) of them.
31. The numbers are used as substitutes for the categories of low, medium, and high, so the numbers are at the
ordinal level of measurement. It does not make sense to compute the average (mean) of such numbers.
32. The numbers are substitutes for names and 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.
Copyright © 2015 Pearson Education, Inc.
Elementary Statistics Using the TI-
83/84 Plus Calculator, 4th edition
ST
Author (s): Mario F. Triola
UV
IA
_A
PP
RO
VE
D?
, Chapter 1: Introduction to Statistics 1
Chapter 1: Introduction to Statistics
Section 1-2 Statistical and Critical Thinking
1. Statistical significance is indicated when methods of statistics are used to reach a conclusion that some
treatment or finding is effective, but common sense might suggest that the treatment or finding 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 a practical significance.
2. If the source of the data can benefit from the results of the study, it is possible that an element of bias is
ST
introduced so that the results are favorable to the source.
3. A voluntary response sample is a sample in which the subjects themselves decide whether to be included in
the study. A voluntary response sample is generally not suitable for a statistical study because the sample
may have a bias resulting from participation by those with a special interest in the topic being studied.
UV
4. Even if we conduct a study and find that there is a correlation, or association, between two variables, we
cannot conclude that one of the variables is the cause of the other.
5. There does appear to be a potential to create a bias.
6. There does not appear to be a potential to create a bias.
IA
7. There does not appear to be a potential to create a bias.
8. There does appear a potential to create a bias.
9. The sample is a voluntary response sample and is therefore flawed.
_A
10. The sample is a voluntary response sample and is therefore flawed.
11. The sampling method appears to be sound.
12. The sampling method appears to be sound.
PP
13. Because there is a 30% chance of getting such results with a diet that has no effect, it does not appear to
have statistical significance, but the average loss of 45 pounds does appear to have practical significance.
14. Because there is only a 1% chance of getting the results by chance, the method appears to have a statistical
significance. The result of 540 boys in 1000 births 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
RO
bother with a procedure that raises the likelihood of a boy from 50% to 54%.
15. Because there is a 23% chance of getting such results with a program that has no effect, the program does
not appear to have statistical significance. Because the success rate of 23% is not much better than the 20%
rate that is typically expected with random guessing, the program does not appear to have practical
significance.
VE
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 point, the program
does not appear to have practical significance.
17. The male and female pulse rates in the same column are not matched in any meaningful way. It does not
make sense to use the difference between any of the pulse rates that are in the same column.
D?
18. Yes, the source of the data is likely to be unbiased.
19. The data can be used to address the issue of whether males and females have pulse rates with the same
average (mean) value.
20. The results do not prove that the populations of males and females have the same average (mean) pulse
rate. The results are based on a particular sample of five males and five females, and analyzing other
samples might lead to a different conclusion. Better results would be obtained with larger samples.
Copyright © 2015 Pearson Education, Inc.
,2 Elementary Statistics Using the TI-83/84 Plus Calculator, 4th edition
21. Yes, each IQ score is matched with the brain volume in the same column, because they are measurements
obtained from the same person. It does not make sense to use the difference between each IQ score and the
brain volume in the same column, because IQ scores and brain volumes use different units of measurement.
For example, it would make no sense to find the difference between an IQ score of 87 and a brain volume
of 1035 cm3.
22. The issue that can be addressed is whether there is a correlation, or association, between IQ score and brain
volume.
23. Given that the researchers do not appear to benefit from the results, they are professionals at prestigious
ST
institutions, and funding is from a U.S. government agency, the source of the data appears to be unbiased.
24. No. Correlation does not imply causation, so a statistical correlation between IQ score and brain volume
should not be used to conclude that larger brain volumes cause higher IQ scores.
25. It is questionable that the sponsor is the Idaho Potato Commission and the favorite vegetable is potatoes.
UV
26. The sample is a voluntary response sample, so there is a good chance that the results are not valid.
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.
28. The correlation, or association, between two variables does not mean that one of the variables is the cause
IA
of the other. Correlation does not imply causation.
29. a. The number of people is (0.39)(1018) = 397.02
b. No. Because the result is a count of people among 1018 who were surveyed, the result must be a whole
_A
number.
c. The actual number is 397 people
255
d. The percentage is = 0.25049 = 25%
1018
PP
30. a. The number of women is (0.38)(427) = 162.26
b. No. Because the result is a count of women among 427 who were surveyed, the result must be a whole
number.
b. The actual number is 162 women.
RO
30
d. The percentage is = 0.07026 = 7%
427
31. a. The number of adults is (0.14)(2302) = 322.28
b. No. Because the result is a count of adults among 2302 who were surveyed, the result must be a whole
number.
VE
c. The actual number is 322 adults.
46
d. The percentage is = 0.01998 = 2%
2302
32. a. The number of adults is (0.76)(2513) = 1909.88
D?
b. No. Because the result is a count of adults among 2513 who were surveyed, the result must be a whole
number.
b. The actual number is 1910 adults.
327
d. The percentage is = 0.13012 = 13%
2513
33. Because a reduction of 100% would eliminate all of the size, it is not possible to reduce the size by 100%
or more.
Copyright © 2015 Pearson Education, Inc.
, Chapter 1: Introduction to Statistics 3
34. If the Club eliminated all car thefts, it would reduce the odds of car theft by 100%, so the 400% figure is
impossible.
35. If foreign investment fell by 100% it would be totally eliminated, so it is not possible for it to fall by more
than 100%.
36. Because a reduction of 100% would eliminate all plague, it is not possible to reduce it by more than 100%.
37. Without our knowing anything about the number of ATVs in use, or the number of ATV drivers, or the
amount of ATV usage, the number of 740 fatal accidents has no context. Some information should be
ST
given so that the reader can understand the rate of ATV fatalities.
38. All percentages of success should be multiples of 5. The given percentage cannot be correct.
39. The wording of the question is biased and tends to encourage negative response. The sample size of 20 is
too small. Survey respondents are self-selected instead of being selected by the newspaper. If 20 readers
UV
respond, the percentages should be multiples of 5, so 87% and 13% are not possible results.
Section 1-3 Types of Data
1. A parameter is a numerical measurement describing some characteristic of a population, whereas a statistic
is a numerical measurement describing some characteristic of a sample.
IA
2. Quantitative data consist of numbers representing counts or measurements, whereas categorical data can be
separated into different categories that are distinguished by some characteristic that is not numerical.
3. Parts (a) and (c) describe discrete data.
4. The values of 1010 and 55% are both statistics because they are based on the sample. The population
_A
consists of all adults in the United States.
5. Statistic 17. Discrete
6. Parameter 18. Discrete
7. Parameter 19. Continuous
PP
8. Statistic 20. Continuous
9. Parameter 21. Nominal
10. Parameter 22. Ratio
RO
11. Statistic 23. Interval
12. Statistic 24. Ordinal
13. Continuous 25. Ratio
14. Discrete 26. Nominal
VE
15. Discrete 27. Ordinal
16. Continuous 28. Interval
29. The numbers are not counts or measures of anything, so they are at the nominal level of measurement, and
it makes no sense to compute the average (mean) of them.
D?
30. The flight numbers do not count or measure anything. They are at the nominal level of measurement, and it
does not make sense to compute the average (mean) of them.
31. The numbers are used as substitutes for the categories of low, medium, and high, so the numbers are at the
ordinal level of measurement. It does not make sense to compute the average (mean) of such numbers.
32. The numbers are substitutes for names and 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.
Copyright © 2015 Pearson Education, Inc.
