STAT 1101 Practice Midterm
Nicholas R. Galbraith
July 23, 2019
Problem 1. A swimsuit manufacturer wants to test the speed of its newly designed suit.
The company designs an experiment by having 6 randomly selected Olympic swimmers swim
as fast as they can with their old swimsuit first and then swim the same event again with
the new, expensive swimsuit. The company will use the difference in times as the response
variable. Criticize the experiment and point out some of the problems with generalizing the
results.
Problem 2. Suppose that my closet contains n pairs of shoes. If I randomly select 2r shoes
(such that
2r < n),
2r
what is the probability that there are no pairs of shoes in my selection?
n
2n
(ans: 2r 2 / 2r .)
Problem 3. Suppose that I toss a die until the first time I observe a 6. What is the
probability that I will toss it more than 5 times?
Problem 4. Suppose that 5% of men and 0.25% of women are colourblind. Suppose I
choose a person at random from the population, and they happen to be colourblind. What
is the probability that they are a man?
Problem 5. A 2001 Danish study published in the Archives of Internal Medicine casts
significant doubt on suggestions that adults who drink wine have higher levels of “good”
cholesterol and fewer heart attacks. These researchers followed a group of individuals born
at a Copenhagen hospital between 1959 and 1961 for 40 years. Their study found that in
this group the adults who drank wine were richer and better educated than those who did
not.
a) What kind of study was this?
b) It is generally true that people with high levels of education and high socioeconomic
status are healthier than others. How does this call into question the supposed health
benefits of wine?
c) Can studies such as these prove causation (that wine helps prevent heart attacks, that
drinking wine makes one richer, that being rich helps prevent heart attacks, etc.)?
Explain.
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Problem 6. A casino knows that people play the slot machines in hopes of hitting the
jackpot but that most of them lose their dollar. Suppose a certain machine pays out an
average of $0.92, with a standard deviation of $120.
a) Why is the standard deviation so large?
b) If you play 5 times, what are the mean and standard deviation of the casino’s profit?
c) If gamblers play this machine 1000 times in a day, what are the mean and standard
deviation of the casino’s profit?
d) Is the casino likely to be profitable? Explain.
Problem 7. A newspaper reports that the governor’s approval rating stands at 65%. The
article adds that the poll is based on a random sample of 972 adults and has a margin of
error of 2.5%. What level of confidence did the pollsters use?
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