ISYE 6644 - Summer 2025/2026 - Final Exam prep Questions and
Answers with Rationales Grade A+ Assured.
Question 1
What is a primary objective of using an indifference-zone normal means selection procedure like
Bechhofer's?
A) To find the normal population with the smallest variance.
B) To guarantee the selection of the best population with 100% certainty.
C) To find the population with the largest mean, especially when it is significantly larger than the
others.
D) To select all populations whose means are statistically similar.
E) To determine the sample size needed for a confidence interval.
Correct Answer: C) To find the population with the largest mean, especially when it is
significantly larger than the others.
Rationale: Indifference-zone procedures are designed to make a correct selection with a high
probability (P) whenever the difference between the best and second-best population means is
greater than a specified amount (δ), which is the indifference zone. The goal is to confidently
identify the best population when it truly stands out.**
Question 2
The Bechhofer procedure for selecting the normal population with the largest mean is a single-
stage procedure. What does this entail?
A) It requires taking observations sequentially until a clear winner emerges.
B) It specifies taking a predetermined number of observations from each population and then
selecting the one with the largest sample mean.
C) It involves creating confidence intervals for each population mean and selecting the one with
the highest upper bound.
D) It is only applicable when there are exactly two competing populations.
E) It requires the user to guess the best population before taking any samples.
Correct Answer: B) It specifies taking a predetermined number of observations from each
population and then selecting the one with the largest sample mean.
Rationale: The Bechhofer procedure is a classic single-stage method. The user specifies the
,[Type here]
desired probability of correct selection (P) and the indifference zone (δ). The procedure then
provides a formula or table to determine the fixed sample size (n) to be taken from each of the k
populations. After taking n samples from each, the population yielding the largest sample mean
is selected as the best.**
Question 3
For which of the following scenarios would a Bernoulli selection procedure be most appropriate?
A) Finding the manufacturing process with the smallest product-to-product variance.
B) Finding the drug that gives the best chance of a cure.
C) Finding the investment strategy with the highest average return.
D) Finding the political candidate with the highest average approval rating.
E) Finding the server configuration with the lowest mean response time.
Correct Answer: B) Finding the drug that gives the best chance of a cure.
Rationale: Bernoulli selection procedures are designed for comparing populations where
the outcome of each observation is a binary success or failure. "Chance of a cure" implies a
success/failure outcome. Smallest variance, highest average return, and lowest mean
response time are problems of normal means or variances, not Bernoulli trials.
Question 4
A Bernoulli selection procedure instructs a researcher to take 100 observations from two
competing drug treatments, A and B. After 100 trials, Drug A results in 85 cures, while Drug B
results in 46 cures. What can be concluded?
A) We cannot be confident that Drug A is better than Drug B.
B) The procedure was flawed because the sample size was too small.
C) Drug A is almost certainly better, and we likely could have stopped the experiment earlier.
D) Both drugs have the same underlying cure probability.
E) Drug B is the better treatment because it has a lower number.
Correct Answer: C) Drug A is almost certainly better, and we likely could have stopped the
experiment earlier.
Rationale: The large difference in the number of successes (85 vs. 46) makes it highly
probable that Drug A has a superior cure rate. Furthermore, such a wide gap suggests that
a sequential procedure, which can stop early when one alternative is clearly superior, might
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have been more efficient and reached the same conclusion with fewer than 100
observations.
Question 5
For which of the following scenarios would a multinomial selection procedure be most
appropriate?
A) Finding the queueing system with the lowest average waiting time.
B) Finding the coin with the highest probability of landing on heads.
C) Finding the most popular of three soft drink brands.
D) Finding the assembly line with the lowest defect rate.
E) Finding the stock with the smallest price variance.
Correct Answer: C) Finding the most popular of three soft drink brands.
Rationale: A multinomial selection procedure is used when each observation falls into one
of k > 2 discrete categories. In this case, each person surveyed will have a preference for
one of the three brands. The goal is to find the category (brand) with the highest
probability of being chosen.
Question 6
When constructing a confidence interval for the mean of an i.i.d. normal sample with an
unknown variance, which probability distribution is most commonly used?
A) The standard normal (Z) distribution.
B) The t-distribution.
C) The chi-squared distribution.
D) The F-distribution.
E) The exponential distribution.
Correct Answer: B) The t-distribution.
Rationale: When the population variance is unknown and must be estimated from the
sample variance (S²), the t-distribution is used to account for the additional uncertainty
introduced by this estimation. The test statistic (X̄ - μ) / (S/√n) follows a t-distribution with
n-1 degrees of freedom.
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Question 7
The paired-t confidence interval for the difference in two means is specifically designed to be
most effective under what condition?
A) The observations from the two populations are completely independent.
B) The sample sizes from the two populations are very large.
C) The observations from the two populations are positively correlated.
D) The variances of the two populations are known and equal.
E) The data from both populations are from a Bernoulli distribution.
Correct Answer: C) The observations from the two populations are positively correlated.
Rationale: The paired-t CI works by analyzing the differences between paired
observations. If the pairs are positively correlated (e.g., a "good" random number stream
for system 1 is also a "good" stream for system 2), the variance of the differences will be
smaller than the sum of the individual variances. This reduction in variance leads to a
tighter (more precise) confidence interval, making it easier to detect a true difference
between the means.
Question 8
What is the primary goal of the Common Random Numbers (CRN) variance reduction
technique?
A) To induce negative correlation between two competing systems.
B) To induce positive correlation between two competing systems to sharpen comparisons.
C) To ensure all observations within a single simulation run are independent.
D) To generate random numbers that follow a normal distribution.
E) To eliminate initialization bias from a steady-state simulation.
Correct Answer: B) To induce positive correlation between two competing systems to
sharpen comparisons.
Rationale: CRN involves using the exact same stream of pseudo-random numbers to
simulate two or more competing systems. This ensures that the systems are being compared
under identical stochastic conditions. By inducing positive correlation, CRN reduces the
variance of the difference between the system performances, resulting in shorter confidence
intervals and more precise comparisons.
Answers with Rationales Grade A+ Assured.
Question 1
What is a primary objective of using an indifference-zone normal means selection procedure like
Bechhofer's?
A) To find the normal population with the smallest variance.
B) To guarantee the selection of the best population with 100% certainty.
C) To find the population with the largest mean, especially when it is significantly larger than the
others.
D) To select all populations whose means are statistically similar.
E) To determine the sample size needed for a confidence interval.
Correct Answer: C) To find the population with the largest mean, especially when it is
significantly larger than the others.
Rationale: Indifference-zone procedures are designed to make a correct selection with a high
probability (P) whenever the difference between the best and second-best population means is
greater than a specified amount (δ), which is the indifference zone. The goal is to confidently
identify the best population when it truly stands out.**
Question 2
The Bechhofer procedure for selecting the normal population with the largest mean is a single-
stage procedure. What does this entail?
A) It requires taking observations sequentially until a clear winner emerges.
B) It specifies taking a predetermined number of observations from each population and then
selecting the one with the largest sample mean.
C) It involves creating confidence intervals for each population mean and selecting the one with
the highest upper bound.
D) It is only applicable when there are exactly two competing populations.
E) It requires the user to guess the best population before taking any samples.
Correct Answer: B) It specifies taking a predetermined number of observations from each
population and then selecting the one with the largest sample mean.
Rationale: The Bechhofer procedure is a classic single-stage method. The user specifies the
,[Type here]
desired probability of correct selection (P) and the indifference zone (δ). The procedure then
provides a formula or table to determine the fixed sample size (n) to be taken from each of the k
populations. After taking n samples from each, the population yielding the largest sample mean
is selected as the best.**
Question 3
For which of the following scenarios would a Bernoulli selection procedure be most appropriate?
A) Finding the manufacturing process with the smallest product-to-product variance.
B) Finding the drug that gives the best chance of a cure.
C) Finding the investment strategy with the highest average return.
D) Finding the political candidate with the highest average approval rating.
E) Finding the server configuration with the lowest mean response time.
Correct Answer: B) Finding the drug that gives the best chance of a cure.
Rationale: Bernoulli selection procedures are designed for comparing populations where
the outcome of each observation is a binary success or failure. "Chance of a cure" implies a
success/failure outcome. Smallest variance, highest average return, and lowest mean
response time are problems of normal means or variances, not Bernoulli trials.
Question 4
A Bernoulli selection procedure instructs a researcher to take 100 observations from two
competing drug treatments, A and B. After 100 trials, Drug A results in 85 cures, while Drug B
results in 46 cures. What can be concluded?
A) We cannot be confident that Drug A is better than Drug B.
B) The procedure was flawed because the sample size was too small.
C) Drug A is almost certainly better, and we likely could have stopped the experiment earlier.
D) Both drugs have the same underlying cure probability.
E) Drug B is the better treatment because it has a lower number.
Correct Answer: C) Drug A is almost certainly better, and we likely could have stopped the
experiment earlier.
Rationale: The large difference in the number of successes (85 vs. 46) makes it highly
probable that Drug A has a superior cure rate. Furthermore, such a wide gap suggests that
a sequential procedure, which can stop early when one alternative is clearly superior, might
,[Type here]
have been more efficient and reached the same conclusion with fewer than 100
observations.
Question 5
For which of the following scenarios would a multinomial selection procedure be most
appropriate?
A) Finding the queueing system with the lowest average waiting time.
B) Finding the coin with the highest probability of landing on heads.
C) Finding the most popular of three soft drink brands.
D) Finding the assembly line with the lowest defect rate.
E) Finding the stock with the smallest price variance.
Correct Answer: C) Finding the most popular of three soft drink brands.
Rationale: A multinomial selection procedure is used when each observation falls into one
of k > 2 discrete categories. In this case, each person surveyed will have a preference for
one of the three brands. The goal is to find the category (brand) with the highest
probability of being chosen.
Question 6
When constructing a confidence interval for the mean of an i.i.d. normal sample with an
unknown variance, which probability distribution is most commonly used?
A) The standard normal (Z) distribution.
B) The t-distribution.
C) The chi-squared distribution.
D) The F-distribution.
E) The exponential distribution.
Correct Answer: B) The t-distribution.
Rationale: When the population variance is unknown and must be estimated from the
sample variance (S²), the t-distribution is used to account for the additional uncertainty
introduced by this estimation. The test statistic (X̄ - μ) / (S/√n) follows a t-distribution with
n-1 degrees of freedom.
, [Type here]
Question 7
The paired-t confidence interval for the difference in two means is specifically designed to be
most effective under what condition?
A) The observations from the two populations are completely independent.
B) The sample sizes from the two populations are very large.
C) The observations from the two populations are positively correlated.
D) The variances of the two populations are known and equal.
E) The data from both populations are from a Bernoulli distribution.
Correct Answer: C) The observations from the two populations are positively correlated.
Rationale: The paired-t CI works by analyzing the differences between paired
observations. If the pairs are positively correlated (e.g., a "good" random number stream
for system 1 is also a "good" stream for system 2), the variance of the differences will be
smaller than the sum of the individual variances. This reduction in variance leads to a
tighter (more precise) confidence interval, making it easier to detect a true difference
between the means.
Question 8
What is the primary goal of the Common Random Numbers (CRN) variance reduction
technique?
A) To induce negative correlation between two competing systems.
B) To induce positive correlation between two competing systems to sharpen comparisons.
C) To ensure all observations within a single simulation run are independent.
D) To generate random numbers that follow a normal distribution.
E) To eliminate initialization bias from a steady-state simulation.
Correct Answer: B) To induce positive correlation between two competing systems to
sharpen comparisons.
Rationale: CRN involves using the exact same stream of pseudo-random numbers to
simulate two or more competing systems. This ensures that the systems are being compared
under identical stochastic conditions. By inducing positive correlation, CRN reduces the
variance of the difference between the system performances, resulting in shorter confidence
intervals and more precise comparisons.
