ISYE 6644 FINAL EXAM QUESTIONS AND VERIFIED CORRECT
ANSWERS || LATEST UPDATE
What is a possible goal of an indifference-zone normal means selection technique? -CORRECT
ANSWER: Find the normal population having the largest mean, especially if the largest mean is
≫ the second-largest.
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. -CORRECT 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. -
CORRECT 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. -
CORRECT 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? -CORRECT 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? -
CORRECT 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? -CORRECT
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 -CORRECT 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? -CORRECT 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. -CORRECT 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. -CORRECT ANSWER:
TRUE
TRUE or FALSE? The common random numbers technique intentionally induces positive
correlation between two systems - much like a paired-𝑡confidence interval. -CORRECT
ANSWER: TRUE
, CRN depends on someone's ability to manipulate the underlying pseudo-random numbers - e.g.,
use the same arrival times when simulating two competing simulated systems. So who ultimately
controls those PRNs?? -CORRECT ANSWER: You do - you are powerful!
TRUE or FALSE? The antithetic random numbers technique intentionally induces negative
correlation between two runs of the same system - this allows us to better estimate the mean of
the system. -CORRECT ANSWER: TRUE
TRUE or FALSE? The control variates technique provides unbiased, low-variance estimates
using a method reminiscent of regression. -CORRECT ANSWER: TRUE
Statistical ranking and selection techniques have been designed to address a variety of
comparison problems. Which ones from the following list?
Find the population having the largest mean.
Find the system with the smallest variance.
Find the alternative with the highest success probability.
Find the most-popular candidate.
All of the above. -CORRECT ANSWER: All of the above.
Suppose we are dealing with i.i.d. normal observations with unknown variance. Which of the
following is true about a 95% confidence interval for the mean μ? -CORRECT ANSWER: We
are 95% sure that our CI will actually contain the unknown value of μ.
We are studying the waiting times arising from two queueing systems. Suppose we make 4
independent replications of both systems, where the systems are simulated independently of each
other.
replication system 1 system2
1 10 25
2 20 10
3 5 40
ANSWERS || LATEST UPDATE
What is a possible goal of an indifference-zone normal means selection technique? -CORRECT
ANSWER: Find the normal population having the largest mean, especially if the largest mean is
≫ the second-largest.
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. -CORRECT 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. -
CORRECT 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. -
CORRECT 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? -CORRECT 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? -
CORRECT 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? -CORRECT
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 -CORRECT 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? -CORRECT 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. -CORRECT 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. -CORRECT ANSWER:
TRUE
TRUE or FALSE? The common random numbers technique intentionally induces positive
correlation between two systems - much like a paired-𝑡confidence interval. -CORRECT
ANSWER: TRUE
, CRN depends on someone's ability to manipulate the underlying pseudo-random numbers - e.g.,
use the same arrival times when simulating two competing simulated systems. So who ultimately
controls those PRNs?? -CORRECT ANSWER: You do - you are powerful!
TRUE or FALSE? The antithetic random numbers technique intentionally induces negative
correlation between two runs of the same system - this allows us to better estimate the mean of
the system. -CORRECT ANSWER: TRUE
TRUE or FALSE? The control variates technique provides unbiased, low-variance estimates
using a method reminiscent of regression. -CORRECT ANSWER: TRUE
Statistical ranking and selection techniques have been designed to address a variety of
comparison problems. Which ones from the following list?
Find the population having the largest mean.
Find the system with the smallest variance.
Find the alternative with the highest success probability.
Find the most-popular candidate.
All of the above. -CORRECT ANSWER: All of the above.
Suppose we are dealing with i.i.d. normal observations with unknown variance. Which of the
following is true about a 95% confidence interval for the mean μ? -CORRECT ANSWER: We
are 95% sure that our CI will actually contain the unknown value of μ.
We are studying the waiting times arising from two queueing systems. Suppose we make 4
independent replications of both systems, where the systems are simulated independently of each
other.
replication system 1 system2
1 10 25
2 20 10
3 5 40
