ISYE 6644
ISYE 6644 Final EXAM 2025
What is a possible goal of an indifference-zone normal means selection technique? -
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. - 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
ISYE 6644
, ISYE 6644
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
TRUE or FALSE? The common random numbers technique intentionally induces
positive correlation between two systems - much like a paired-𝑡confidence interval. -
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?? - 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. - ANSWER-TRUE
TRUE or FALSE? The control variates technique provides unbiased, low-variance
estimates using a method reminiscent of regression. - 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. - 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? - ANSWER-We
are 95% sure that our CI will actually contain the unknown value of μ.
ISYE 6644
ISYE 6644 Final EXAM 2025
What is a possible goal of an indifference-zone normal means selection technique? -
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. - 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
ISYE 6644
, ISYE 6644
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
TRUE or FALSE? The common random numbers technique intentionally induces
positive correlation between two systems - much like a paired-𝑡confidence interval. -
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?? - 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. - ANSWER-TRUE
TRUE or FALSE? The control variates technique provides unbiased, low-variance
estimates using a method reminiscent of regression. - 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. - 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? - ANSWER-We
are 95% sure that our CI will actually contain the unknown value of μ.
ISYE 6644
