ISYE 6644 - FINAL PREP Questions with Correct Solutions
Question:
1. 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 k largest mean is the
second-largest.
Question:
2. 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
Question:
3. 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
Question:
4. 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).
Question:
5. 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.
Question:
6. For which scenarios(s) below might it be appropriate to use a multinomial selection
procedure?
Answer:
Find the most-popular political candidate.
Question:
7. 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 en- Æ try for k=3, P^ =0.90, and Æ θ^ =1.4.
Question:
8. 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
Question:
9. 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
Question:
10. 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.}
, Question:
11. 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
Question:
12. TRUE or FALSE? The common random numbers technique intentionally induces positive
correlation between two systems - much like a paired- confidence interval.
Answer:
TRUE 5a
Question:
13. 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!
Question:
14. 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
Question:
15. TRUE or FALSE? The control variates technique provides unbiased, low-variance
estimates using a method reminiscent of regression.
Answer:
TRUE
Question:
16. 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.
Question:
1. 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 k largest mean is the
second-largest.
Question:
2. 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
Question:
3. 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
Question:
4. 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).
Question:
5. 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.
Question:
6. For which scenarios(s) below might it be appropriate to use a multinomial selection
procedure?
Answer:
Find the most-popular political candidate.
Question:
7. 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 en- Æ try for k=3, P^ =0.90, and Æ θ^ =1.4.
Question:
8. 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
Question:
9. 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
Question:
10. 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.}
, Question:
11. 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
Question:
12. TRUE or FALSE? The common random numbers technique intentionally induces positive
correlation between two systems - much like a paired- confidence interval.
Answer:
TRUE 5a
Question:
13. 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!
Question:
14. 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
Question:
15. TRUE or FALSE? The control variates technique provides unbiased, low-variance
estimates using a method reminiscent of regression.
Answer:
TRUE
Question:
16. 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.
