Practice exam questions, exam 2, STAT2301
Multiple Choice:
1) A home monitoring company claims to be able to respond to alarms on average in
5 mins. A random sample of 50 alarm incidents has a mean response time of 7 mins
with a 95% confidence interval for the true mean response time of (6.1, 7.9) mins.
Which of the following statements is true?
(a) Most homeowners can expect response times of 5 mins.
(b) 95% of the time, response times are between 6.1 and 7.9 mins.
(c) If we were to repeat this study many times, in about 95% of studies, the
confidence interval would contain 5 mins.
(d) If we were to repeat this study many times, in about 95% of studies, the
confidence interval would contain 7 mins.
(e) None of the above are true.
2) Which of the following statements about the central limit theorem is FALSE?
(a) if n is large then the distribution of the sample mean can be approximated closely
by a normal curve
(b) if n is large, then the variance of the sample mean is smaller than the variance of
the original observations.
(c) The mean of the sample means is the same as the population mean.
(d) if n is large, then the sampling distribution of the sample size can be
approximated closely by a normal curve
(e) If the parent population is symmetric the central limit theorem gives good
approximations even for small n such as 10.
3) A demographer, using a random sample of n = 500 people, obtained a 95 percent
confidence interval for mean age at marriage () in years for US adults. The CI was
(26.4, 27.3). Suppose another demographer obtained a separate independent sample
of n=500 people and also constructed a 95% confidence interval for the same quantity
, what can we say about this new interval as compared to the previous one?
a.
b.
c.
d.
e.
narrower and would be less likely to contain .
wider and would be more likely to contain .
narrower and would be more likely to contain .
It may be wider or narrower, but it has same chance to contain .
narrower but we can’t be sure if it would be more or less likely to contain
.
4) Suppose we have two events A, and B such that P(A)=0.5, P(B)=0.5 and P(A and
B)=0.4. Which of the following statements are true?
i. P(A | B) = 0.2.
ii. A and B are dependent events.
iii. A and B are disjoint.
a.
b.
c.
d.
e.
(i), (ii) and (iii)
(ii) only
(ii) and (iii) only
(i) only
(i) and (ii) only
The next six questions relate to the following problem. A couple has three children.
Assume that boys and girls are equally likely and that gender is independent from child to
child.
5) Let A be the event that the couple only has boys. Then P(A) is
(a)
(b)
(c)
(d)
(e)
1/4
2/3
1/8
3/4
1/2
6) Let B be the event that the gender of the first child is the same as the gender of the
third child. Then P(B) is
(a)
(b)
(c)
(d)
(e)
3/4
1/2
3/10
1/4
1
7) Let C be the event that the couple’s first child is a girl. Then P(C ) is
(a) 1/2
(b) 2/3
(c) 3/4
(d) 1/4
(e) 1/3
8) The probability of “A and B” is
(a) 1/8
(b) 1/2
(c) 1/3
(d) 2/3
(e) 0
9) The probability of “A and C” is
(a) 1/4
(b) 1/2
(c) 1/8
(d) 2/3
(e) 0
10) Which of the following statements is true?
(a)
(b)
(c)
(d)
(e)
A is independent of B and independent of C.
A is dependent on B but independent of C.
A is independent of B, but dependent on C.
A is dependent on both B and C.
We do not have enough information to judge dependence of A in relation to B or
C.
11) Suppose a company is considering a new system to catch employees who have taken
a drug. Suppose that the system is in fact faulty, and that it only detects 90% of
employees who have taken the drug, and also gives a false positive for 5% of “innocent”
employees. (That is 5% of employees who have actually not taken the drug will
incorrectly get a positive result, and 90% of those who have will correctly register as
having a positive result.)
Suppose also that in fact 10% of all employees have actually taken the drug. If a
randomly chosen employee registers a negative result on the test, the actual chance that
the employee really has taken the drug is given by;
(a) 67%
(b) 75%
(c) 1.2%
(d) 55%
(e) 3.3%
True/False
12) Each of the following statements is either True or False. Indicate which by circling
the letter T or the letter F. Do not give any explanation.
T F (a) Suppose a 95% confidence interval for  is (12, 19). Then we know the sample
mean is 15.5.
T F (b) Suppose a 95% confidence interval for  is (12, 19). Then we will claim that 
is between 12 and 19. We also state that we are using a method which gives correct
claims in 95% of samples.
T F (c) A 99% confidence interval will be wider than a 95% confidence interval, when
calculated on the same data set.
T F (d) If A and B are disjoint then P(A and B) is 1.
T F (e) If A and B are independent then P(A and B) = 0