ISYE 6644 FINAL EXAM NEWEST 2024 COMPLETE 200
QUESTIONS AND CORRECT DETAILED ANSWERS
(VERIFIED ANSWERS) |ALREADY GRADED
A+||BRAND NEW VERSION!
What is a possible goal of an indifference-zone normal means selection technique? 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. 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. 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. 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? 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?
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?
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 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? 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. 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. TRUE
TRUE or FALSE? The common random numbers technique intentionally induces positive
correlation between two systems - much like a paired-𝑡confidence interval. 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?? 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. TRUE
TRUE or FALSE? The control variates technique provides unbiased, low-variance estimates using
a method reminiscent of regression. 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.
QUESTIONS AND CORRECT DETAILED ANSWERS
(VERIFIED ANSWERS) |ALREADY GRADED
A+||BRAND NEW VERSION!
What is a possible goal of an indifference-zone normal means selection technique? 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. 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. 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. 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? 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?
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?
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 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? 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. 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. TRUE
TRUE or FALSE? The common random numbers technique intentionally induces positive
correlation between two systems - much like a paired-𝑡confidence interval. 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?? 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. TRUE
TRUE or FALSE? The control variates technique provides unbiased, low-variance estimates using
a method reminiscent of regression. 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.
