ISYE 6644 FINAL EXAM QUESTIONS AND ANSWERS ALREADY GRADED A+
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
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
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
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
