 Consider two events, A and B. Suppose that P(A) = 90% and P(B) = 60%. Which of the
following must be true?
 The area under the normal curve between 1 and +2 is closest to
 A certain list of numbers has mean 100 and SD 10. The fraction of numbers in the list
between 80 and 120 is
The next three questions refer to an article by H. Seppala, M.D., T. Klaukka, M.D., J.
VuopioVarkila, M.D., and 4 others in the 14 August 1997 issue of The New England
Journal of Medicine. The article is entitled The effect of changes in the
consumption of macrolide antibiotics on erythromycin resistance in group A streptococci in
Finland.
Erythromycin is an antibiotic of macrolide type. One thing erythromycin is used for is
to treat some streptococcal infections, especially in people who are allergic to
penicillin (streptococci are the kind of bacteria responsible for "strep
throat," among other infections). A worldwide concern is that antibiotics are being
overprescribed, and that their widespread will lead to the proliferation of strains of
bacteria that are resistant to the antibiotics, so antibiotics will become less effective.
A particular danger is the phenomenon of "crossresistance:" exposure to one
antibiotic can select for bacteria that are resistant not only to it, but also to related
antibiotics.
The use of erythromycin in Finland roughly tripled in the 1980s, reaching a peak of
about 3 daily defined doses per 1000 inhabitants per day in 1988. In the early 1990s,
tests on throat (pharyngeal) cultures and pus samples from Finnish patients nationwide
showed that about 13% of group A streptococci were resistant to erythromycin, a
substantial increase from 19881989 (about 5% were resistant then). The increase was
highly publicized, and Finnish physicians were taught about the risks and possible
alternatives to prescribing erythromycin for respiratory and skin infections. After the
publicity, there was a decrease in the prescription of macrolide antibiotics (of which
erythromycin is one), measured by the number of defined daily doses per 1000 inhabitants
per day. Since 1992, the number of defined daily doses of macrolide antibiotics per 1000
inhabitants has varied between about 1.28 and 1.74. Before 1990, the only macrolide
antibiotic used in Finland was erythromycin; others are now even more frequently
prescribed than erythromycin.
The authors, which include the Finnish Study Group for Antimicrobial Resistance,
analyzed the erythromycin resistance of group A streptococci isolated from 39,247 throat
and pus samples obtained between 1991 and 1996. At most one sample per patient per year
was used, if the patient could be identified. The proportion of erythromycinresistant
group A streptococci had increased from about 5% in 19881989 to about 13% in 1990. After
the reduction in the prescription of erythromycin, the relative frequency of
erythromycinresistant group A streptococci increased to 16.5% in 1992, and to 19.0% in
1993, then began falling, to 15.6% in 1994, to 10.0% in 1995, and to 8.6% in 1996. The
authors analyze these data using a variety of statistical techniques.
 Let us agree to call this an "experiment," because a policy was deliberately
introduced to decrease the amount of macrolide antibiotics used in Finland.
 i) If a decrease in the amount of erythromycin prescribed does cause a decrease in the
fraction of erythromycinresistant group A streptococci, population size would tend to
confound with the apparent effect of defined daily doses per 1000 population.
ii) A secular trend in the proportion of erythromycinresistant group A streptococci would
tend to confound with the apparent effect of defined daily doses per 1000 population.
 i) Bacteria reproduce very quickly, so one might expect selective pressures on their
breeding to act quickly. Because the proportion of erythromycinresistant group A
streptococci continued to climb for several years after the number of defined daily doses
per 1000 inhabitants per day had started to fall, and because it took 5 years after the
prescription of erythromycin was reduced before the proportion of erythromycinresistant
group A streptococci fell below the 1989 level, it is quite likely that the association
between reducing the use of the antibiotic and the proportion of resistant bacteria is
spurious.
ii) This work addresses the proportion of erythromycinresistant group A
streptococci rather than the number of such streptococci, so it might be that the
number of erythromycinresistant group A streptococci was actually smallest when the
prescription rate was highest.
 We play a game in which I give you a list of numbers, and you give me back a single
number, not necessarily one of the numbers in the list.
I pay you
$100  (the sum of the absolute values of
the differences between the numbers in the list and the number you give me)
To get the most money, you should pick
 The SD of a certain list is zero.
 A certain list of 100 numbers has mean equal to one and median equal to one.
 What characteristics of a scatterplot does the following regression residual plot
reveal?
 With reference to the residual plot in the previous question,
 A certain list of numbers has a histogram that is approximated well by a normal curve.
The mean of the list is 100, and the SD is 20. The 97.5th percentile of the list is
closest to
 Which of the following has a distribution that is skewed to the left?
 Which theory of probability would be best suited to assign meaning to the statement
"the chance of a magnitude 7 or greater earthquake on the Hayward fault by
the year 2020 is
10%?"
 (i) According to the subjective theory of probability, what I mean when I say that the
chance a coin lands heads is 50% is that I believe that the chance the coin lands heads is
50%.
(ii) According to the frequency theory of probability, what it means to say that the
chance a coin lands heads is 50% is that for any number a>0, there is a number of
tosses sufficiently large that if I toss the coin under essentially identical conditions
that many times or more,
 (#heads)/(#tosses)  50%  < a.
The next six questions refer to the following table of
fictitious observations of the midterm scores of 6 students, and the time they took (in
minutes) to work the midterm.
Score (points) 
70 
90 
80 
100 
60 
80 
Time (minutes) 
80 
50 
60 
60 
70 
40 
The average time is 60 minutes, with an SD
of 12.9 minutes. In standard units, the list of times is {1.55, 0.78, 0, 0, 1.55, 0.78
}.
 The SD of the exam scores is closest to
 The upper quartile of the exam scores is:
 The IQR of the exam scores is:

The RMS of the exam scores is closest to:

The correlation coefficient of the times and exam scores is closest to:
 Let r denote the correlation coefficient of scores and times,
and let SD_{s} be the SD of the scores.
The regression line would predict that the score of a person who
took 72.9 minutes to work the exam would be
 I toss each of 1000 coins until it lands headsup. The average number of tosses it
takes, not counting the final toss that results in "heads," is 1. The largest
number of coins for which it could have taken 20 or more tosses before
the toss that yielded the
first head is closest to