Page 1 of 34
ISYE 6644 FINAL PREP EXAM PRACTICE
QUESTIONS WITH VERIFIED SOLUTIONS
GRADED A+ TESTED AND APPROVED!!!
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.
, Page 2 of 34
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
singlestage 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.
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.
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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.
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
4 30 30
Assuming that the average waiting time results from each replication are
approximately normal, find a two-sided 95% CI for the difference in the means
of the two systems. -- ANSWER--This is a two-sample CI problem assuming
unknown and unequal variances. We have
[-29.76, 9.76]
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This is sort of the same as Question 2, except we have now used common
random numbers to induce positive correlation between the results of the two
systems. Again find a two-sided 95% CI for the difference in the means of the
two systems. -- ANSWER--This is a paired-t CI problem assuming unknown
variance of the differences.
[-16.5, -3.5]
Suppose A and B are two identically distributed, unbiased, antithetic estimators
for the mean μ of some random variable, and let C = ( A + B ) / 2. Which of the
following is true? -- ANSWER--E [ C ] = μ and V a r ( C ) < V a r ( A ) / 2.
Suppose that you want to pick that one of three normal populations having the
largest mean. We'll assume that the variances of the three competitors are all
known to be equal to σ 2 = 4. (Ya, I know that this is a crazy, unrealistic
assumption, but let's go with it anyway, okey dokey?) I want to choose the best
of the three populations with probability of correct selection of 95% whenever
the best population's mean happens to be at least δ = 1 larger than the
secondbest population's. How many observations from each population does
Bechhofer's procedure N B tell me to take before I can make such a conclusion?
-- ANSWER--Using the notation of the notes, we want to make sure to get the
right answer with probability of P = 0.95 whenever μ [ k ] − μ [ k − 1 ] ≥ δ =
1.
We simply go to NB's table with k = 3 and δ / σ = to obtain a sample size
of n = 30 from each population.
ISYE 6644 FINAL PREP EXAM PRACTICE
QUESTIONS WITH VERIFIED SOLUTIONS
GRADED A+ TESTED AND APPROVED!!!
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.
, Page 2 of 34
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
singlestage 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.
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.
, Page 3 of 34
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.
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
4 30 30
Assuming that the average waiting time results from each replication are
approximately normal, find a two-sided 95% CI for the difference in the means
of the two systems. -- ANSWER--This is a two-sample CI problem assuming
unknown and unequal variances. We have
[-29.76, 9.76]
, Page 4 of 34
This is sort of the same as Question 2, except we have now used common
random numbers to induce positive correlation between the results of the two
systems. Again find a two-sided 95% CI for the difference in the means of the
two systems. -- ANSWER--This is a paired-t CI problem assuming unknown
variance of the differences.
[-16.5, -3.5]
Suppose A and B are two identically distributed, unbiased, antithetic estimators
for the mean μ of some random variable, and let C = ( A + B ) / 2. Which of the
following is true? -- ANSWER--E [ C ] = μ and V a r ( C ) < V a r ( A ) / 2.
Suppose that you want to pick that one of three normal populations having the
largest mean. We'll assume that the variances of the three competitors are all
known to be equal to σ 2 = 4. (Ya, I know that this is a crazy, unrealistic
assumption, but let's go with it anyway, okey dokey?) I want to choose the best
of the three populations with probability of correct selection of 95% whenever
the best population's mean happens to be at least δ = 1 larger than the
secondbest population's. How many observations from each population does
Bechhofer's procedure N B tell me to take before I can make such a conclusion?
-- ANSWER--Using the notation of the notes, we want to make sure to get the
right answer with probability of P = 0.95 whenever μ [ k ] − μ [ k − 1 ] ≥ δ =
1.
We simply go to NB's table with k = 3 and δ / σ = to obtain a sample size
of n = 30 from each population.
