Seeing Through Statistics
5th Edition by Jessica M. Utts
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included (Ch 1 to 27)
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UTTS, SEEING THROUGH STATISTICS, 5E, 2025 9780357757550; CHAPTER 1: THE BENEFITS AND
RISKS OF USING STATISTICS
TABLE OF CONTENTS
Answers to Exercise Questions .................................................................................................................. 1
Answers to Reflection Questions ............................................................................................................... 9
Answers to Mini Projects ........................................................................................................................... 9
ANSWERS TO EXERCISE QUESTIONS
1. Explain why the relationship shown in Table 1.1, concerning the use of aspirin and heart attack
rates, can be used as evidence that aspirin.
Answer:
Because the men were randomly assigned to the two conditions (i.e., because it was a randomized
experiment), the only substantial difference between the two groups should have been whether
they took aspirin or a placebo. Therefore, the observed reduction in heart attack rates for those
taking aspirin can be attributed to the difference in treatments.
2. “People who often attend cultural activities, such as movies, sports events and concerts, are more
likely than their less cultured cousins to survive the next eight to nine years, even when education
and income are taken into account, according to a survey by the University of Umea in Sweden”
(American Health, April 1997, p. 20).
a. Can this claim be tested by conducting a randomized experiment? Explain.
b. On the basis of the study that was conducted, can we conclude that attending cultural events
makes people more likely to live longer? Explain.
c. The article continued, “No one’s sure how Mel Gibson and Mozart help health, but the
activities may enhance immunity or coping skills.” Comment on the validity of this
statement.
d. The article notes that education and income were taken into account. Give two examples of
other factors about the people surveyed that you think should also have been taken into
account. (Hint: These should be factors that might differ for those who do and don’t attend
cultural events, and also could be related to longevity.)
Answer:
a. No. People cannot be randomly assigned to attend cultural events over a long period of time
or not.
, b. We cannot conclude that the relationship is causal because this is an observational study.
There could be other factors that account for the increased longevity. For instance, maybe
those who are already healthier are more likely to attend cultural events.
c. The statement implies that there is a causal connection and seeks an explanation. The causal
link is not justified.
d. Examples are general health at the start of the study and amount of exercise in their daily
lives. (Maybe those who are healthier and who have more energy are more likely to exercise
and to attend cultural events.) Another example is level of income. Those with higher income
may be more able to afford cultural events, and may also have better access to other resources
that increase longevity.
3. Explain why the number of people in a sample is an important factor to consider when designing
a study.
Answer:
If the measurements of interest are extremely variable in nature, or if the difference between
groups is very small, then a large sample will be required in order to detect real differences
between groups or treatments.
4. Explain what problems may arise in trying to make conclusions based on a survey sent to the
subscribers of a specialty magazine. Find or construct an example.
Answer:
First, even if they all responded to the survey, the results would apply only to subscribers to that
magazine, and not to some larger population. Second, it is very unlikely that a large proportion
will respond, and those who do are most likely to have strong opinions. Therefore, the results
cannot even be extended to all subscribers of that magazine.
5. “If you have borderline high blood pressure, taking magnesium supplements may help, Japanese
researchers report. Blood pressure fell significantly in subjects who got 400–500 milligrams of
magnesium a day for four weeks, but not in those getting a placebo” (USA Weekend, 22–24 May
1998, p. 11).
a. Do you think this was a randomized experiment or an observational study? Explain.
b. Do you think the relationship found in this study is a causal one, in which taking magnesium
actually causes blood pressure to be lowered? Explain.
Answer:
a. It was most likely a randomized experiment. Placebos are not likely to be taken in
observational studies.
b. The relationship is probably causal. If the participants were randomly assigned to take
magnesium or a placebo, other factors between the two groups should be about equal, so any
differences are likely to be caused by taking the magnesium versus taking the placebo.
6. A study similar to the one in Example 1.4 was reported in the May 17, 2012, issue of The New
England Journal of Medicine. The researchers followed people for an average of 13 years and
found that people who consumed two or more cups of coffee a day were less likely to die during
the course of the study than those who drank no coffee.
, a. Was this study a randomized experiment or an observational study? Explain how you know.
b. Based on this study, can it be concluded that drinking coffee causes people to live longer?
c. The following headlines appeared on news websites reporting these results. In each case,
explain whether or not the conclusion in the headline is justified.
i. “Association of coffee drinking with total and cause-specific mortality” (Source:
https://www.coffeeandhealth.org/research/association-of-coffee-drinking-with-total-
andcause-specific-mortality)
ii. “NIH Study: Coffee Really Does Make You Live Longer, After All” (Source:
http://www.theatlantic.com/health/archive/2012/05/nih-study-coffee-really-does-
make-you-livelonger- after-all/257302/)
Answer:
a. It was an observational study. Coffee drinking over many years cannot be randomly assigned.
b. No. A cause and effect conclusion cannot be made based on an observational study. There are
likely to be other differences between those who drink coffee and those who do not, and
perhaps those other differences have an effect on how long someone lives.
c. Headline (i) is justified because it does not imply a causal relationship. Headline (ii) is not
justified because it does imply a causal relationship.
