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Statistics

David Freedman, Robert Pisani, Roger Purves

Chapter 2

Observational Studies - all with Video Answers

Educators

Chapter Questions

02:25

Problem 1

The Federal Bureau of Investigation reports state-level and national data on crimes. 17
(a) An investigator compares the incidence of crime in Minnesota and in Michigan in 2001 , there 3.584 crimes in Minnesota, compared to $4,082$ in Michigan. He concludes that Minnesotans are more law- abiding. After all, Michigan includes the big bad city of Detroit. What do you say?
(b) An investigator compares the incidence of crime in the U.S. in 1991 and 2001 . In $1991,$ there $28,000$ crimes, compared to $22,000$ in $2001 .$ She concludes that the U.S. became more law-abiding over that time period. What do you say?

Bryan Luo
Bryan Luo
Numerade Educator
04:15

Problem 2

The National Highway and Traffic Safety Administration analyzed thefts of new cars in $2002,$ as well as sales for that year. $^{18}$
(a) There were 99 Corvettes stolen, and 26 Infiniti $Q 45$ sedans. Should you conclude that American thieves prefer American cars? Or is something missing from the equation?
(b) There were 50 BMW 7 -series cars cars cors compared to 146 in the 3 -series. Should you conclude that thieves prefer smaller cars, which are more economical to run and easier to park? Or is something missing from the equation?
(c) There were 429 Liberty Jeeps stolen, compared to $207,991$ sold, for a rate of 2 per $100,000 .$ True or false and explain: the rate is low because the denominator is large.

Heena Haldankar
Heena Haldankar
Numerade Educator
02:13

Problem 3

From table 1 in chapter $1(\mathrm{p} .6),$ those children whose parents refused to participate in the randomized controlled Salk trial got polio at the rate of 46 per $100,000 .$ On the other hand, those children whose parents consented to participation got polio at the slightly higher rate of 49 per $100,000$ in the treatment group and control group taken together. Suppose that this field trial was repeated the following year. On the basis of the figures, some parents refused to allow their children to participate in the experiment and be exposed to this higher risk of polio. Were they right? Answer yes or no, and explain briefly.

Bryan Luo
Bryan Luo
Numerade Educator
03:32

Problem 4

The Public Health Service studied the effects of smoking on health, in a large sample of representative households. 19 For men and for women in each age group, those who had never smoked were on average somewhat healthier than the current smokers, but the current smokers were on average much healthier than those who had recently stopped smoking.
(a) Why did they study men and women and the different age groups separately?
(b) The lesson seems to be that you shouldn't start smoking, but once you've started, don't stop. Comment briefly.

Heena Haldankar
Heena Haldankar
Numerade Educator
02:20

Problem 5

There is a rare neurological disease (idiopathic hypoguesia) that makes food taste bad. It is sometimes treated with zinc sulfate. One group of investigators did two randomized controlled experiments to test this treatment. In the first trial, the subjects did not know whether they were being given the zinc sulfate or a placebo. However, the doctors doing the evaluations did know. In this trial, patients on zinc sulfate improved significantly; the placebo group showed little improvement. The second trial was run double-blind: neither the subjects nor the doctors doing the evaluation were told who had been given the drug or the placebo. In the second trial, zinc sulfate had no effect. Should zinc sulfate be given to treat the disease? Answer yes or no, and ex- plain briefly.

Bryan Luo
Bryan Luo
Numerade Educator
02:23

Problem 6

(Continues the previous exercise.) The second trial used what is called a "crossover"" design. The subjects were assigned at random to one of four groups:
$\begin{array}{ll}{\text { placebo }} & {\text { placebo }} \\ {\text { placebo }} & {\text { zinc }} \\ {\text { zinc }} & {\text { placebo }} \\ {\text { zinc }} & {\text { zinc }}\end{array}$
In the first group, the subjects stayed on the placebo through the whole experiment. In the second group, subjects began with the placebo, but haffway through the experiment they were switched to zinc sulfate. Similarly, in the third group, subjects began on zine sulfate but were switched to placebo. In the last group, they stayed on zinc sulfate. Subjects knew the design of the study, but were not told the group to which they were assigned.
Some subjects did not improve during the first half of the experiment. In each of the four groups, these subjects showed some improvement (on average) during the second half of the experiment. How can this be explained?

Heena Haldankar
Heena Haldankar
Numerade Educator
03:48

Problem 7

According to a study done at Kaiser Permanente in Walnut Creek, California, users of oral contraceptives have a higher rate of cervical cancer than non- users, even after adjusting for age, education, and marital status. Investigators concluded that the pill causes cervical cancer.".
(a) Is this a controlled experiment or an observational study?
(b) Why did the investigators adjust for age? education? marital status?
(c) Women using the pill were likely to differ from non-users on another factor which affects the risk of cervical cancer. What factor is that?
(d) Were the conclain briefly. no, and explain briefly.

Bryan Luo
Bryan Luo
Numerade Educator
02:07

Problem 8

Ads for ADT Security Systems claim $^{22}$
When you go on vacation, burglars go to work.... According to FBI statistics, over 25$\%$ of home burglaries occur between Memorial Day and Labor Day.
Do the statistics prove that burglars go to work when other people go on
vacation? Answer yes or no, and explain briefly.

Heena Haldankar
Heena Haldankar
Numerade Educator
03:04

Problem 9

People who get lots of vitamins by eating five or more servings of fresh fruit and vegetables each day (especially "cruciferous" vegetables like broccoli) have much lower death rates from cancer and lung cancer, according to many observational studies. These studies were so encouraging that two randomized controlled experiments were done. The treatment groups were given large doses of vitamin supplements, while people in the contrrol groups just ate their usual dict. One experiment looked at colon cancer; the other, at lung cancer.
The first experiment found no difference in the death rate from colon calon cancer between the treatment group and the control group. The second experiment found that beta carotene (as a diet supplement) increased the death rate from lung cancer. $^{23}$ True or false, and explain:
(a) The experiments confirmed the results of the observational studies.
(b) The observational studies could easily have reached the wrong conclusions, due to confounding- people who eat lots of fruit and vegetables have lifestyles that are different in many other ways too.

Bryan Luo
Bryan Luo
Numerade Educator
04:07

Problem 10

A study of young children found that that that that that mith more body fat tended to have more "controlling" mothers; the San Francisco Chronicle concluded that "Parents of Fat Kids Should Lighten Up."
(a) Was this an observational study or a randomized controlled experiment?
(b) Did the study find an association between mother's behavior and her child's level of body fat?
(c) If controlling behavior by the mother causes children to eat more, would that explain an association between controlling behavior by the mother and her child's level of body fat?
(d) Suppose there is a gene which causes obesity. Would that explain the association?
(e) Can you think of another way to explain the association?
(f) Do the data support the Chronicle's advice on child-rearing? Discuss briefly.

Heena Haldankar
Heena Haldankar
Numerade Educator
03:34

Problem 11

California is evaluating a new program to rehabilitate prisoners before their release; the object is to reduce the recidivism rate- the percentage who will be back in prison within two years of release. The program involves several months of "boot camp"- military-style basic training with very strict
discipline. Admission to the program is voluntary. According to a prison spokessman, "Those who complete boot camp are less likely to return to prison than other inmates."."
(a) What is the treatment group in the prison spokesman's comparison? the control group?
(b) Is the prison spokesman's comparison based on an observational study or a randomized controlled experiment?
(c) True or false: the data show that boot camp worked. Explain your answers.

Bryan Luo
Bryan Luo
Numerade Educator
04:38

Problem 12

(Hypothetical.) A study is carried out to determine the effect of party affili-ation on voting behavior in a certain city. The city is divided up into wards. In each ward, the percentage of registered Democrats who vote is higher than the percentage of registered Republicans who vote. True or false: for the city
as a whole, the percentage of registered Democrats who vote must be higher
than the percentage of registered Republicans who vote. If true, why? If false, give an example.

Heena Haldankar
Heena Haldankar
Numerade Educator