COMS 5583 COMPLETE EXAM REVIEW
WITH FULL SOLUTIONS
●● TRUE or FALSE? The Bechhofer procedure for selecting the normal
population with the largest mean specifies the appropriate number of
observations to take from each competing population, and simply selects
the competitor having the largest sample mean.
Answer: True
●● TRUE or FALSE? Sometimes a single-stage procedure like
Bechhofer's is inefficient. In fact, it's possible to use certain sequential
procedures that take observations one-at-a-time (instead of all at once in
a single stage) to make good selection decisions using fewer
observations.
Answer: True
●● For which scenarios(s) below might it be appropriate to use a
Bernoulli selection procedure?
a) Find the inventory policy having the largest profit.
b) Find the drug giving the best chance of a cure.
c) Find the maintenance policy having the lowest failure probability.
d) Find the scheduling rule that that has the best chance of making an
on-time delivery.
Answer: All three of (b), (c), and (d).
,●● Suppose that a Bernoulli selection procedure tells you to take 100
observations from each of two populations, A and B. It turns out that A
gets 85 successes and B gets 46 successes. What do you think?
Answer: 1) A almost certainly has a higher success probability than B.
2) We could've probably stopped sampling a bit earlier (i.e., with fewer
than 100 observations) because A was so far ahead of B.
●● For which scenarios(s) below might it be appropriate to use a
multinomial selection procedure?
Answer: Find the most-popular political candidate.
●● Suppose that we want to know which of Coke, Pepsi and Dr.pepper
is the most popular. We would like to make the correct selection with
probability of at least P*=0.90 in the event that the ration of the highest-
to-second-highest preference probabilities happens to be at least 0*=1.4.
How many people does the single-stage procedure Mbem require us to
interview?
Answer: 126
Go to the table in the notes and pick off the entry for k=3, P^⋆=0.90, and
θ^⋆=1.4.
●● Which of the following parameters can you get confidence intervals
for?
Means
, Variances
Quantiles
Differences between the means of two systems
Answer: All of the above
●● If we have an iid normal sample of observations, X1, X2,...Xn, what
probability distribution is most-commonly used to obtain cofidence
intervals for the mean?
Answer: t
●● TRUE or FALSE? The paired CI for the differences in two means is
designed to work especially well if all of the observations from the first
population are completely independent of all of the observations from
the second population.
Answer: FALSE. {In fact, it's easier to distinguish between the two
means if Xi is positively correlated with Yi. Think about my parallel
parking example in the class notes.}
●● TRUE or FALSE? You can use a version of independent replications
to obtain confidence intervals for the difference in the means from two
simulation models.
Answer: TRUE
WITH FULL SOLUTIONS
●● TRUE or FALSE? The Bechhofer procedure for selecting the normal
population with the largest mean specifies the appropriate number of
observations to take from each competing population, and simply selects
the competitor having the largest sample mean.
Answer: True
●● TRUE or FALSE? Sometimes a single-stage procedure like
Bechhofer's is inefficient. In fact, it's possible to use certain sequential
procedures that take observations one-at-a-time (instead of all at once in
a single stage) to make good selection decisions using fewer
observations.
Answer: True
●● For which scenarios(s) below might it be appropriate to use a
Bernoulli selection procedure?
a) Find the inventory policy having the largest profit.
b) Find the drug giving the best chance of a cure.
c) Find the maintenance policy having the lowest failure probability.
d) Find the scheduling rule that that has the best chance of making an
on-time delivery.
Answer: All three of (b), (c), and (d).
,●● Suppose that a Bernoulli selection procedure tells you to take 100
observations from each of two populations, A and B. It turns out that A
gets 85 successes and B gets 46 successes. What do you think?
Answer: 1) A almost certainly has a higher success probability than B.
2) We could've probably stopped sampling a bit earlier (i.e., with fewer
than 100 observations) because A was so far ahead of B.
●● For which scenarios(s) below might it be appropriate to use a
multinomial selection procedure?
Answer: Find the most-popular political candidate.
●● Suppose that we want to know which of Coke, Pepsi and Dr.pepper
is the most popular. We would like to make the correct selection with
probability of at least P*=0.90 in the event that the ration of the highest-
to-second-highest preference probabilities happens to be at least 0*=1.4.
How many people does the single-stage procedure Mbem require us to
interview?
Answer: 126
Go to the table in the notes and pick off the entry for k=3, P^⋆=0.90, and
θ^⋆=1.4.
●● Which of the following parameters can you get confidence intervals
for?
Means
, Variances
Quantiles
Differences between the means of two systems
Answer: All of the above
●● If we have an iid normal sample of observations, X1, X2,...Xn, what
probability distribution is most-commonly used to obtain cofidence
intervals for the mean?
Answer: t
●● TRUE or FALSE? The paired CI for the differences in two means is
designed to work especially well if all of the observations from the first
population are completely independent of all of the observations from
the second population.
Answer: FALSE. {In fact, it's easier to distinguish between the two
means if Xi is positively correlated with Yi. Think about my parallel
parking example in the class notes.}
●● TRUE or FALSE? You can use a version of independent replications
to obtain confidence intervals for the difference in the means from two
simulation models.
Answer: TRUE
