Stat 20
S.M. Stoyanov
Fall 2017
Final exam Version 2: Answers
PART I: Questions 1-10 are worth 2 points each. You do NOT need to show your
work, and NO partial credit will be given. Indicate your choice by CIRCLING the
option you choose. If nothing is circled, we will mark the problem wrong.
A pharmaceutical company developed a new treatment for eczema and performed a double-blind randomized
experiment to see if it worked better than the company’s old treatment. The new treatment performed better in the
experiment. The p-value was
10%
. Label the following statements as true or false by circling T or F.
1. We can reject the null hypothesis.
T

2. There is an 10% chance that the null hypothesis is true.
T

Suppose we draw 2 tickets at random without replacement from a box with tickets marked
{
1, 2, 3, . . . , 9
}
.
Let
A
be the event that at least one of the tickets drawn is labeled with an even number, let
B
be the event
that at least one of the tickets drawn is labeled with a prime number (recall that the number 1 is not regarded
as a prime number).
3. Are
A
C
and
B
C
mutually exclusive?

4. Suppose the numbers on the tickets drawn are 3 and 9. Which of the following events occur?
(i)
A
(ii)
B
(iii)
A
∩
B
(iv)
A
C
∩
B
(v)
A
∩
B
C

5. The heights from the NHANES 2009-2010 data followed the normal curve closely, with a mean of about 167
cm. About 2,000 of the 2,926 adults surveyed had heights between 157 cm and 177 cm. The SD of the heights
was
(a)
about 10 cm
(b) smaller than 10 cm
(c) larger than 10 cm
(d) impossible to say with the information given.

6. An investigator performs a two-sided test of significance on his data, and finds that the
z
-score of his test
statistic is about 1.9. This means that

7. Consider events
A
and
B
such that the unconditional probability of
A
is 65%, and the unconditional probability
of
B
is 35%. Then,
P
(
A
∩
B
) is closest to:
B

8. A 1995 study on income and nativity looked at the fraction of the state populations that have high incomes
(greater than $50,000 per year), and the fraction of the state populations that are born outside the United
States. The correlation across the 50 states is 0.52, indicating that the foreign-born US residents, on the whole,
have higher incomes than the native-born residents.