Copyright 2022 Pearson Education, Inc.

Copyright © 2022 Pearson Education, Inc.

Chapter 1: Introduction to Statistics

Section 1-1: Statistical and Critical Thinking

• 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.

• The sample consists of the 1046 adults who were surveyed. The population consists of all adults.
• 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.

• 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.

• 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 per capita consumption of margarine and the divorce rate in Maine.

• Yes, there does appear to be a potential to create a bias.
• No, there does not appear to be a potential to create a bias.
• No, there does not appear to be a potential to create a bias.
• Yes, there does appear to be a potential to create a bias.
• The sample is a voluntary response sample and has strong potential to be flawed.
• 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.

• The sampling method appears to be sound.
• The sampling method appears to be sound.
• The Ornish weight loss program has statistical significance, because the results are so unlikely (3 chances in

1000) to occur by chance. It does not have practical significance because the amount of lost weight (3.3 lb) is so small.

• Because there is only one chance in a thousand of getting such success rates by chance, the difference does

appear to have statistical significance. The 92% success rate for surgery appears to be substantially better than the 72% success rate for splints, so the difference does appear to have practical significance.

• The difference between Mendel’s 25% rate and the result of 26% is not statistically significant. According to

Mendel’s theory, 145 of the 580 peas would have yellow pods, but the results consisted of 152 peas with yellow pods. The difference of 7 peas with yellow pods among the 580 offspring does not appear to be statistically significant. The difference does not appear to have practical significance.

• 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.

• With 40 out of 41 ballots having the Democrat first, it appears that the result is statistically significant. Because

of the great advantage enjoyed by Democrats, the results also have practical significance.

• Because it is so unlikely (0.3%) to get these results by chance, the results have statistical significance. With

about 57% (from 235/414) of the coin toss winners going on to win the game, the result appears to have practical significance.

• There appears to be statistical significance given the large discrepancy between 79.1% and 39%. Because the

results are so far from yielding a jury of peers, it appears that the results have practical significance.

• With only a 0.0000006% chance of getting such results, it appears that the results are statistically significant.

The discrepancy between the 61% rate for voters who actually did vote and the 70% rate of those who said that they voted is a fairly large discrepancy, and the results appear to have practical significance.(Elementary Statistics Using Excel, 7e Mario Triola) (Solution Manual, For Complete File, Download link at the end of this File) 1 / 4

2 Chapter 1: Introduction to Statistics

Copyright © 2022 Pearson Education, Inc.

• Yes. Each column of 8 AM and 12 AM temperatures is recorded from the same subject, so each pair is

matched.

• No. The source is from university researchers who do not appear to gain from distorting the data.
• The data can be used to address the issue of whether there is a correlation between body temperatures at
• 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.

• Because the differences could easily occur by chance (with a 64% chance), the differences do not appear to

have statistical significance.

• No. The lemon imports are weights in metric tons and the crash fatality rates are fatalities per 100,000

population, so their differences are meaningless.

• The issue that can be addressed is whether there is a correlation, or association, between lemon imports and

crash fatality rates.

• No. The author of an article for the Journal of Chemical Information and Modeling has no reason to collect or

present the data in a way that is biased.

• No. Correlation does not imply causation, so a statistical correlation between lemon imports and crash fatality

rates should not be used to conclude that lemon imports are the cause of fatal crashes.

• It is questionable that the sponsor is the Idaho Potato Commission and the favorite vegetable is potatoes.
• 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.

• 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.

• 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.

• 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.

• 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.

• The sample is a voluntary response sample, so there is a good chance that the results do not accurately reflect

the larger population.

• Because the nutritionists are paid such large amounts of money, they might be more inclined to find favorable

results. It is very possible that the results represent desired outcomes instead of actual outcomes.

• a. 700 adults
• 55%
• a. 253.31 subjects
• No. Because the result is a count of people among the 347 who were surveyed, the result must be a whole

number.

• 253 subjects
• 32%
• a. 559.2 respondents
• 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.

• 559 respondents
• 8%
• a. 847.56 drivers
• No. Because the result is a count of respondents saying that they text while driving, the result must be a

whole number.

• 848 drivers
• Given that texting while driving is extremely dangerous, the result of 42% of drivers who text while driving

is far too high. The result suggests that steps should be taken to substantially lower that rate. 2 / 4

Section 1-2: Types of Data 3

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• Because a reduction of 100% would eliminate all of the size, it is not possible to reduce the size by 100% or

more.

• 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.

• Because a reduction of 100% would eliminate all plaque, it is not possible to reduce it by more than 100%.
• Because a reduction of 100% would eliminate all car thefts, it is not possible to reduce it by more than 100%.
• 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.

• 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.

• All percentages of success should be multiples of 5. The given percentages cannot be correct.

Section 1-2: Types of Data

• The population consists of all adults in the United States, and the sample is the 1001 adults who were surveyed.

Because the value of 69% refers to the sample, it is a statistic.

• quantitative
• categorical
• categorical
• quantitative
• Only part (b) describes discrete data.
• The sample is the 36,000 adults who were surveyed. The population is all adults in the United States.
• statistic
• ratio
• discrete
• statistic
• parameter
• parameter
• statistic
• statistic
• statistic
• parameter
• parameter
• continuous
• continuous
• discrete
• discrete
• continuous
• discrete
• discrete
• continuous
• nominal
• ordinal
• ordinal
• ratio
• interval
• nominal
• ratio
• interval
• 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.

• 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).

• The temperatures are at the interval level of measurement. Because there is no natural starting point with

0F representing “no heat,” ratios such as “twice” make no sense, so it is wrong to say that it is twice as warm in Paris as it is in Anchorage.

• 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 Harvard and MIT is the same as the difference between Stanford and the University of California at Berkeley.

• a. Continuous, because the number of possible values is infinite and not countable.
• Discrete, because the number of possible values is finite.
• Discrete, because the number of possible values is finite.
• Discrete, because the number of possible values is infinite and countable. 3 / 4

4 Chapter 1: Introduction to Statistics

Copyright © 2022 Pearson Education, Inc.

• Interval level of measurement. The direction of north represented by 0 is arbitrary, and 0 does not represent

“no direction.” Differences between degrees are meaningful; the difference between 30 and 60 is the same as the difference between 150 and 180 . But ratios are not meaningful; the ratio of 60 to 30 does not result in twice some direction. (These degree measurements are directions, not amounts of rotation.)

Section 1-3: Collecting Sample Data

• The study is an experiment because subjects were given treatments.
• The subjects in the study did not know whether they were given the magnet treatment or the sham treatment,

and those who administered the treatments also did not know.

• The group sample sizes are large enough so that the researchers could see the effects of the two treatments, but

it would have been better to have larger samples.

• The sample appears to be a convenience sample. Given that the subjects were all patients at a Veterans Affairs

hospital, it is not likely that the sample is representative of the population, so it is questionable whether the results can be generalized for the population of subjects with chronic low back pain.

• 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.

• The study is an observational study because the subjects were not given any treatment.
• 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.

• Answers vary, but the following are good possibilities.
• Obtain a printed copy of the class roster, assign consecutive numbers (integers), then use a computer to

randomly generate six of those numbers.

• Select every third student leaving class until six students are chosen.
• Randomly select three males and three females.
• 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.)

• Select the first six students who enter the class.
• systematic
• convenience
• random
• stratified
• cluster
• random
• stratified
• systematic
• random
• cluster
• convenience
• systematic
• 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.

• 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.

• 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.

• Observational study. The sample of only three students is too small.
• Experiment. The biased sample created by using a small sample of college students cannot be fixed by using a

larger sample. The larger sample will still be a biased sample that is not representative of the population of all adults.

• 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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