1. (a) The investigator should be comparing crime rates (number
of crimes per 100,000 people, say) rather than simple numbers of
crimes. If Minnesota has substantially more people than Michigan
(which is in fact true), the crime rate in Michigan may be lower
than in Minnesota (which is also true).
1. (b) Because the population of the U.S. very likely increased
over that period, the crime rate probably fell an even larger
percentage of the 1991 figure than the simple number of crimes
did. So it is fair to say that the U.S. became more law-abiding
in that period.
2. (a) Something is missing: How many of each kind of car are
on the road? If there are many more Corvettes, then they are easier
to find and steal than Infiniti sedans.
2. (b) Same reasoning: Are there more 3-series (which I assume are
the smaller ones, but I don't know that for sure) than 7-series?
If so, the percentage of 3-series stolen may be smaller than the
percentage of 7-series stolen.
2. (c) True, at least in part. The rate is also low because
the numerator (the number stolen) is small. (The author says
false, and phrases it differently: The rate is low because the
numerator is small relative to the denominator. Okay, whatever.)
3. No. We know that the first-year parents who consented were usually better off economically, and hence their children, if left untreated, were more likely to get polio than those whose parents didn't consent. The treatment lowered the risk of polio almost to the level of the children of non-consenting parents. (But the second-year parents did not know there was a difference in risk between first-year consenters and non-consenters, so they were not being foolish in refusing consent, just uninformed.)
4. (a) To avoid confounding factors, since smoking may affect differently people of different sexes and/or ages. This study was controlling for the confounding variables age and sex. (see p. 13) 4. (b) This is the wrong conclusion to draw from the evidence. The assignment to the various groups was far from random: each subject chose which group he/she was in. Many people choose to stop smoking because they are getting sick. Thus, stopping smoking was probably the effect, not the cause, of health problems. ("Association is not causation" again.)
12. False (or rather, conclusion unjustified): Simpson's paradox may be at work here. Example: Suppose the city has two wards. In Ward A, 50% of the 100 Democrats and 40% of the 1000 Republicans vote. In Ward B, 20% of the 1000 Democrats and 10% of the 100 Republicans vote. So (50+200)/1100 = 22.7% of the Democrats in the city vote, while (400+10)/1100 = 37.3% of the Republicans in the city vote.