1. Nine students in a science class separately weighed a
small object on the same
scale. The weights (in grams) recorded by each student
are shown below.
6.2 6.0 6.0 15.3 6.1 6.3 6.2 6.329 6.2
The students want to determine as accurately as they can
the actual weight of this
object. Of the following methods, which would you
recommend they use?
a. Use the most common number, which is 6.2
b. Use the 6.329 since it includes more decimal places.
c. Add up the 9 numbers and divide by 9.
d. Throw out the 15.3, add up the other 8 numbers and
divide by 8.
2. The following message is printed on a bottle of
prescription medication:
WARNING: For application to skin areas there
is a 15%
chance of developing a rash. If a rash
develops, consult
your physician.
Which of the following is the best interpretation of this
warning?
a. Don’t use the medication on your skin-- there’s a good
chance of
developing a rash.
b. For application to the skin, apply only 15% of the
recommended dose.
c. If a rash develops, it will probably involve only 15%
of the skin.
d. About 15 of 100 people who use this medication develop
a rash.
e. There is hardly a chance of getting a rash using this
medication.
3. The Springfield Meteorological Center wanted to determine
the accuracy of
their weather forecasts. They searched their records for
those days when forecasts
had reported a 70% chance of rain. They compared their
forecasts to records of
whether or not it actually rained on those particular days.
The forecast of 70% chance of rain can be considered very
accurate if it rained
on:
a. 95%-100% of those days.
b. 85%-94% of those days.
c. 75%-84% of those days.
d. 65%-74% of those days.
e. 55%-64% of those days.
4. A teacher wants to change the seating arrangement in her
class in the hopes that it
will increase the number of comments her students make.
She first decides to see
how many comments students make with the current seating
arrangement. A
record of the number of comments made by her 8 students
during one class period
is shown below.
____ _Student Initials
_
A.A R.F. A.G. J.G. C.K.
N.K. J.L. A.W.
Number of
Comments 0 5 2 22 3
2 1 2 .
She wants to summarize this data by computing the typical
number of comments
made that day. Of the following methods, which would you
recommend she use?
a. Use the most common number, which is 2.
b. Add up the 8 numbers and divide by 8.
c. Throw out the 22, and then add up the other 7 and
divide by 7.
d. Throw out the 0, add up the other 7 numbers and divide
by 7.
For items 5-6
A new medication is being tested to determine its
effectiveness in the treatment of
eczema, an inflammatory condition of the skin. Thirty
patients with eczema were selected
to participate in the study. The patients were randomly
divided into two groups. Twenty
patients in an experimental group received the medication,
while ten patients in a control
group received no medication. The results after two months
are shown below.
Experimental group (medication)
Control group (no medication)
Improved 8
Improved 2
No improvement 12
No Improvement 8
5. Based on the data, I think the medication was:
a. somewhat effective
b. basically ineffective
6. If you chose option a, select the one If
you chose option b, select the
explanation below that best describes one
explanation below that best
your reasoning.
describes your reasoning.
a. 40% of the people (8/20) in the
a. In the control group,
experimental group improved.
two people improved

even without medication.
b. 8 people improved in the experimental
b. In the experimental group,
group while only 2 improved in the
more people didn’t get
control group
better than did (12 vs. 8).
c. In the experimental group, the number
c. The difference between
of people who improved is only 4 less
the numbers who
than the number who didn’t improve
improved and didn’t
(12-8), while in the control group the
improve is about the
difference is 6 (8-2).
same in each group

(4 vs. 6).
d. 40% of the patients in the
d. Only 40% of the patients in
experimental group improved (8/20),
the experimental group
while only 20% improved in the
improved (8/20), while 20%.
control group (2/10).
improved in the control

group (2/10).
Items 7-9
Listed below are several possible reasons one might question
the results of the
experiment described above. Mark A for every reason you
agree with.
A = Agree B = Disagree
7. It’s not possible to compare the two groups because
there are different
numbers of patients in each group.
8. With a sample size of 30, it’s possible that random
assignment of patients may
have, just by chance, placed the most severe cases in
one of the groups.
9. I’m not given enough information about how doctors
decided whether or
not patients improved. Doctors may have been biased in
their judgment.
10. Two containers, labeled A and B, are filled with red and
blue marbles in the
following quantities.
Container Red
Blue
A 6
4
B 60
40
Each container is shaken vigorously. After choosing one
of the containers, you
will reach in, without looking, draw out a marble. If the
marble is blue, you win
$50. Which container gives you the best chance of drawing
a blue marble?
a. Container A (with 6 red and 4 blue)
b. Container B (with 60 red and 40 Blue)
c. Equal chances from each container.
11. Which of the following sequences is most likely to
result from flipping a fair coin
five times? (H=Heads, T=Tails)
a. H H H T T
b. T H H T H
c. T H T T T
d. H T H T H
e. All four are equally likely
Items 12-15
Select one or more explanations for possible coin-flipping
outcomes.
A = Agree B = Disagree
12. Since coin flipping is random, the coin ought to
alternate frequently
between landing heads and tails.
13. If you repeatedly flipped a coin five times, each of
the sequences would
occur about as often as any sequence.
14. If you get a couple of heads in a row, the probability
of tails on the next
flip increases.
15. Every sequence of five flips has exactly the same
probability of occurring.
17. Listed below are the same sequences of H’s and T’s
that were listed in Item 11.
Which of the sequences is least likely to result from
flipping a coin 5 times?
a. H H H T T
b. T H H T H
c. T H T T T
d. H T H T H
e. All four sequences are equally unlikely
Items 17-22
A marketing research company was asked to determine
how much money
teenagers (ages 13-19) spend on recorded music
(cassette tapes, CD’s, and
DVD’s). The company randomly selected 80 malls
located around the country.
A field researcher stood in a central location in
the mall and passers-by who
appeared to be the approximate age were asked to
fill out the questionnaire. A
total of 2,050 questionnaires were completed by
teenagers. On the basis of this
survey, the research company reported that the
average teenager in this country
spends $155 each year on recorded music.
Listed below are several statements concerning the survey.
Mark A for each statement
you agree with. Mark B for each statement you disagree with.
A = Agree B = Disagree
17. The average is based on teenagers’ estimates of what
they spend and therefore
could be quite different from what teenagers actually
spend.
18. They should have done the survey at more than 80 malls
if they wanted an
average based on teenagers throughout the country.
19. The sample of 2,050 teenagers is too small to permit
drawing a conclusion about the
entire country.
20. They should have asked teenagers coming out of music stores.
21. The average could be a poor estimate of the spending of
all teenagers given that
teenagers were not randomly chosen to fill out the
questionnaire.
22. The average could be a poor estimate of the spending of
all teenagers given that only
teenagers in malls were sampled.
23. Five faces of a fair die are painted black, and one face
is painted white. The die is
rolled six times. Which of the following results is more
likely?
a. Black side up on five of the rolls; white side
up on the other roll
b. Black side up on all six rolls
c. a and b are equally likely
24. Half of all newborn children are girls and half are
boys. Hospital A records an
average of 50 births a day. Hospital B records an
average of 10 births a day. On a
particular day, which hospital is more likely to record
80% or more female births.
a. Hospital A (with 50 births a day)
b. Hospital B (with 10 births a day)
c. The two hospitals are equally likely to record such
an event.
25. The Caldwells want to buy a new car, and they have
narrowed their choices to a
Buick or an Oldsmobile. They first consulted an issue of
Consumer Reports, which
compared rates of repairs for various cars. Records or
repairs done on 400 cars of
each type showed somewhat fewer mechanical problems with
the Buick than the
Oldsmobile.
The Caldwells then talked to three friends, two
Oldsmobile owners, and one former
Buick Owner. Both Oldsmobile owners reported having a
few mechanical problems,
but nothing major. The Buick owner, however, exploded
when asked how he liked
his car:
“First the fuel injection went out-- $250
bucks. Next I started
having trouble with the rear end and had to
replace it. I
finally decided to sell it after the
transmission went. I’d never
buy another Buick.”
The Caldwells want to buy the car that is less likely to
require major repair work.
Given what they currently know, which car would you
recommend that they buy?
a. I would recommend they buy the Oldsmobile,
primarily because of all
the trouble their friend had with his Buick.
Since they haven’t heard
similar horror stories about an Oldsmobile,
they should go with it.
b. I would recommend they buy the Buick in spite of
their friend’s bad
experience. This is just one case, while the
information reported in
Consumer Report is based on many cases. And
according to the data,
the Buick is somewhat less likely to require
repairs.
c. I would tell them that it didn’t matter which
car they bought. Even
though one of the models might be more
likely than the other to require
repairs, they could still, just by chance,
get stuck with a particular car
that would need a lot of repairs. They may
as well toss a coin to decide.
26. Forty college students participated in a study of
the effect of sleep on test scores.
Twenty of the students volunteered to stay up all
night studying the night before
the test (no sleep group). The other 20 students
(the control group) went to bed
by 11:00 p.m. on the evening of the test. The test
scores for each group are shown
in the graphs below. Each dot on the graph
represents a particular student’s score.
For example, the two dots above 80 in the bottom
graph indicate that two students
in the sleep group scored 80 on the test.
. . . . .
. . . . .
. . . . . . . .
. .
30 40 50 60 70
80 90 100
Test Scores: No- Sleep Group
. . .
. . . . .
.
. . . . . . . . .
. .
30 40 50 60 70
80 90 100
Test Scores: Sleep Group
Examine the two graphs carefully. Then choose from the 6
possible conclusions listed
below the one you most agree with.
a. The no-sleep group did better because none of these
students scored below 40 and, a
student in this group achieved the highest score.
b. The no-sleep group did better because its average appears
to be a little higher than the
average of the sleep group.
c. There is no difference between the two groups because
there is considerable overlap in
the scores of the two groups.
d. There is no difference between the two groups because the
difference between their
averages is small compared to the amount of variation in
the scores.
e. The sleep group did better because its average appears to
be a little higher than the
average of the no sleep group.
Items 27-31
For one month, 500 elementary students kept a daily record
of the hours spent watching
television. The average number of hours per week spent
watching television was 28.
The researchers conducting the study also obtained report
cards for each of the students.
They found that the students who did well in school spent
less time watching television
than those students who did poorly.
Listed below are several possible statements concerning the
results of this research.
Mark A for each statement you agree with.
A = Agree B = Disagree
27. The sample of 500 is too small to permit drawing
conclusions.
28. If a student decreases the amount of time spent
watching television, his or her
performance in school would improve.
29. Even though students who did well watched less
television, this doesn’t
necessarily mean that watching television hurts
school performance.
30. One month is not a long enough period of time to
estimate how many hours the
students really spend watching television.
31. The research demonstrates that watching television
causes poorer performance in
school.
Items 32-37
The school committee of a small town wanted to determine the
average number of
children per household in their town. They divided the total
number of children in the
town by 50, the total number of households. Indicate which
statements must be true if
the average number of children per household is exactly 2.2.
Mark A for the statements you agree with and B for the
statements you disagree with.
A = Agree B = Disagree
32. Half of the households in the town have more than 2
children.
33. More households in the town have 3 children than
have 2 children.
34. There are 110 children in the town.
35. There are 2.2 children in the town for every adult.
36. The most common number of children in a household is 2.
37. More households in the town have 2 children than
have 3 children.
38. When two dice are simultaneously thrown it is possible
that one of the following
two results occurs:
Result 1: A 5 and a 6 are obtained.
Result 2: A 5 is obtained twice.
Select the response that you agree with most:
a. The chance of obtaining each of these results is
equal.
b. There is more chance of obtaining Result 1.
c. There is more chance of obtaining Result 2.
d. It is impossible to give an answer.
39. When three dice are simultaneously thrown, which of the
following results is
MOST LIKELY to be obtained?
a. Result 1: A 5, a 3 and a 6
b. Result 2: A 5 three times
c. Result 3: A 5 twice and a 3
d. All three results are equally likely
40. When three dice are simultaneously thrown, which of
these three results is
LEAST LIKELY to be obtained?
a. Result 1: A 5, a 3 and a 6
b. Result 2: A 5 three times
c. Result 3: A 5 twice and a 3
d. All three results are equally unlikely