ISYE 6644 Exam 3 Practice Questions - Spring 2026 Complete
Study Guide with Verified Questions, Answers & Rationales.
Georgia Institute Of Technology - 130 Questions and Answers
Already Graded A+ Premium Exam Tested And Verified
Subject Area Industrial Engineering / Operations Research (Simulation)
Description This practice exam covers advanced topics in discrete-event simulation, including
input modeling, output analysis, variance reduction, and optimization. Designed
to test deep conceptual understanding and application of simulation methodology.
Expected Grade A+
Total Questions 130
Duration 3 hours
Learning Outcomes 1. Apply goodness-of-fit tests and select appropriate input distributions
2. Analyze simulation output using confidence intervals and batch means
3. Implement variance reduction techniques (common random numbers, antithetic
variates, control variates)
4. Design and interpret simulation experiments, including factorial designs
5. Assess the impact of initialization bias and warm-up periods on output analysis
Accreditation Georgia Institute of Technology, College of Engineering
Page 1
,1. A simulation analyst observes that the sample mean of a steady-state output
process is heavily influenced by the initial transient. To reduce bias in the point
estimator, the analyst decides to delete an initial sequence of observations. Which of
the following methods is most appropriate for determining the truncation point?
A. Welch's graphical procedure based on moving averages
B. The method of batch means with a fixed number of batches
C. The autoregressive order determination method
D. The maximum likelihood estimation of the steady-state mean
Answer: A. Welch's graphical procedure based on moving averages
Welch's graphical procedure is specifically designed to identify the warm-up period by
plotting moving averages of the output process and visually detecting when the series
stabilizes. Batch means (B) is for output analysis after truncation, not for determining
truncation. Autoregressive order (C) is for time series modeling. Maximum likelihood
(D) assumes a parametric model and does not directly address initialization bias.
2. In a simulation of a manufacturing system, the analyst uses the technique of
common random numbers (CRN) to compare two system configurations. After
running 10 independent replications, the paired-difference confidence interval for
the difference in mean throughput is computed as (2.5, 1.5). Which of the following
conclusions is valid at the 95% confidence level?
A. There is a statistically significant difference between the two configurations because the
interval includes zero.
B. The first configuration has a significantly higher mean throughput because the interval is
symmetric around -0.5.
C. The second configuration has a significantly higher mean throughput because the interval
contains negative values.
D. There is insufficient evidence to conclude that the two configurations have different mean
throughputs.
Answer: D. There is insufficient evidence to conclude that the two configurations
have different mean throughputs.
Since the confidence interval includes zero, we cannot reject the null hypothesis that the
mean difference is zero. Thus, there is no statistically significant difference at the 95%
level. Options A, B, and C misinterpret the inclusion of zero: including zero means no
significance, not that one is higher.
Page 2
,3. A simulation model of a call center uses an exponential distribution with mean 2
minutes for service times. After collecting 1000 service times, the analyst performs a
chi-square goodness-of-fit test with 10 equally probable intervals. The test statistic is
15.2. Using = 0.05, what is the appropriate conclusion? (The critical value for ² with
9 degrees of freedom is 16.92, and with 10 degrees of freedom is 18.31.)
A. Reject the null hypothesis because the test statistic exceeds the critical value for 9 degrees
of freedom.
B. Fail to reject the null hypothesis because the test statistic is less than the critical value for
9 degrees of freedom.
C. Reject the null hypothesis because the test statistic exceeds the critical value for 10
degrees of freedom.
D. Fail to reject the null hypothesis because the test statistic is less than the critical value for
10 degrees of freedom.
Answer: B. Fail to reject the null hypothesis because the test statistic is less than
the critical value for 9 degrees of freedom.
For a chi-square goodness-of-fit test with k intervals and r estimated parameters,
degrees of freedom = k - 1 - r. Here, the exponential distribution has one parameter
(rate) estimated from data, so r = 1. With 10 intervals, df = 10 - 1 - 1 = 8. However, the
problem gives critical values for 9 and 10 df, suggesting they omitted the parameter
estimation. Typically, without parameter estimation, df = 9 (10-1). The test statistic 15.2
< 16.92, so we fail to reject H0. The correct answer is B.
4. A simulation analyst is estimating the mean waiting time in a queue. Using the
method of independent replications, 20 replications yield a sample mean of 5.2
minutes and a sample standard deviation of 1.8 minutes. Assuming the replication
means are approximately normally distributed, what is the half-width of the 95%
confidence interval for the true mean waiting time? (t_{0.025,19} = 2.093)
A. 0.842
B. 0.842 minutes
C. 0.842 minutes
D. 0.842 minutes
Answer: A. 0.842
The half-width is t_{/2, n-1} * s / n = 2.093 * (1.) = 2.093 * (1..472) = 2.093 *
0.4025 = 0.842. Options B, C, D are identical except for wording; A is the numeric
value. The question is flawed but the intended correct answer is the numeric half-width.
Page 3
, 5. In a simulation experiment, the analyst uses a 2^k factorial design to study the
effects of three factors: arrival rate (A), service rate (B), and number of servers (C).
The estimated main effects are: A = 2.3, B = 1.5, C = 0.8. The interaction effects are:
AB = 0.6, AC = 0.2, BC = 0.1, ABC = 0.05. Which of the following interpretations is
correct?
A. Factor A has the largest impact on the response, and there is a strong interaction between
A and B.
B. Factor B has the largest impact because its effect is negative, indicating it reduces the
response.
C. The interaction ABC is negligible, so all two-way interactions can be ignored.
D. Factor C has the smallest main effect, and the AB interaction is practically significant
relative to the main effects.
Answer: D. Factor C has the smallest main effect, and the AB interaction is
practically significant relative to the main effects.
The magnitude of main effect A is 2.3, B is 1.5, C is 0.8, so C has the smallest main
effect. The AB interaction (0.6) is about 40% of the B main effect, which is practically
significant. Option A is incorrect because AB (0.6) is not strong compared to A (2.3).
Option B is incorrect because magnitude matters, not sign. Option C is incorrect
because negligible three-way interaction does not imply two-way interactions are
negligible.
6. A simulation model uses a linear congruential generator (LCG) with parameters:
modulus m = 2^31 1, multiplier a = 7^5, and increment c = 0. The generator is used
to produce uniform(0,1) random numbers. Which of the following statements about
this generator is true?
A. The generator has full period because c = 0 and m is prime.
B. The generator is a multiplicative LCG with period m1 when the seed is relatively prime to
m.
C. The generator will fail the spectral test because a is a power of 7.
D. The generator produces numbers with poor uniformity because c = 0.
Answer: B. The generator is a multiplicative LCG with period m1 when the seed is
relatively prime to m.
This is a multiplicative LCG (c=0). With modulus m prime and a a primitive root
modulo m, the period is m-1. Here, m = 2^31-1 is a Mersenne prime, and 7^5 is a
known primitive root, so period = m-1. Option A is incorrect because full period for
multiplicative LCG is m-1, not m. Option C is not necessarily true; spectral test
depends on a. Option D is false; uniformity can still be good.
Page 4
Study Guide with Verified Questions, Answers & Rationales.
Georgia Institute Of Technology - 130 Questions and Answers
Already Graded A+ Premium Exam Tested And Verified
Subject Area Industrial Engineering / Operations Research (Simulation)
Description This practice exam covers advanced topics in discrete-event simulation, including
input modeling, output analysis, variance reduction, and optimization. Designed
to test deep conceptual understanding and application of simulation methodology.
Expected Grade A+
Total Questions 130
Duration 3 hours
Learning Outcomes 1. Apply goodness-of-fit tests and select appropriate input distributions
2. Analyze simulation output using confidence intervals and batch means
3. Implement variance reduction techniques (common random numbers, antithetic
variates, control variates)
4. Design and interpret simulation experiments, including factorial designs
5. Assess the impact of initialization bias and warm-up periods on output analysis
Accreditation Georgia Institute of Technology, College of Engineering
Page 1
,1. A simulation analyst observes that the sample mean of a steady-state output
process is heavily influenced by the initial transient. To reduce bias in the point
estimator, the analyst decides to delete an initial sequence of observations. Which of
the following methods is most appropriate for determining the truncation point?
A. Welch's graphical procedure based on moving averages
B. The method of batch means with a fixed number of batches
C. The autoregressive order determination method
D. The maximum likelihood estimation of the steady-state mean
Answer: A. Welch's graphical procedure based on moving averages
Welch's graphical procedure is specifically designed to identify the warm-up period by
plotting moving averages of the output process and visually detecting when the series
stabilizes. Batch means (B) is for output analysis after truncation, not for determining
truncation. Autoregressive order (C) is for time series modeling. Maximum likelihood
(D) assumes a parametric model and does not directly address initialization bias.
2. In a simulation of a manufacturing system, the analyst uses the technique of
common random numbers (CRN) to compare two system configurations. After
running 10 independent replications, the paired-difference confidence interval for
the difference in mean throughput is computed as (2.5, 1.5). Which of the following
conclusions is valid at the 95% confidence level?
A. There is a statistically significant difference between the two configurations because the
interval includes zero.
B. The first configuration has a significantly higher mean throughput because the interval is
symmetric around -0.5.
C. The second configuration has a significantly higher mean throughput because the interval
contains negative values.
D. There is insufficient evidence to conclude that the two configurations have different mean
throughputs.
Answer: D. There is insufficient evidence to conclude that the two configurations
have different mean throughputs.
Since the confidence interval includes zero, we cannot reject the null hypothesis that the
mean difference is zero. Thus, there is no statistically significant difference at the 95%
level. Options A, B, and C misinterpret the inclusion of zero: including zero means no
significance, not that one is higher.
Page 2
,3. A simulation model of a call center uses an exponential distribution with mean 2
minutes for service times. After collecting 1000 service times, the analyst performs a
chi-square goodness-of-fit test with 10 equally probable intervals. The test statistic is
15.2. Using = 0.05, what is the appropriate conclusion? (The critical value for ² with
9 degrees of freedom is 16.92, and with 10 degrees of freedom is 18.31.)
A. Reject the null hypothesis because the test statistic exceeds the critical value for 9 degrees
of freedom.
B. Fail to reject the null hypothesis because the test statistic is less than the critical value for
9 degrees of freedom.
C. Reject the null hypothesis because the test statistic exceeds the critical value for 10
degrees of freedom.
D. Fail to reject the null hypothesis because the test statistic is less than the critical value for
10 degrees of freedom.
Answer: B. Fail to reject the null hypothesis because the test statistic is less than
the critical value for 9 degrees of freedom.
For a chi-square goodness-of-fit test with k intervals and r estimated parameters,
degrees of freedom = k - 1 - r. Here, the exponential distribution has one parameter
(rate) estimated from data, so r = 1. With 10 intervals, df = 10 - 1 - 1 = 8. However, the
problem gives critical values for 9 and 10 df, suggesting they omitted the parameter
estimation. Typically, without parameter estimation, df = 9 (10-1). The test statistic 15.2
< 16.92, so we fail to reject H0. The correct answer is B.
4. A simulation analyst is estimating the mean waiting time in a queue. Using the
method of independent replications, 20 replications yield a sample mean of 5.2
minutes and a sample standard deviation of 1.8 minutes. Assuming the replication
means are approximately normally distributed, what is the half-width of the 95%
confidence interval for the true mean waiting time? (t_{0.025,19} = 2.093)
A. 0.842
B. 0.842 minutes
C. 0.842 minutes
D. 0.842 minutes
Answer: A. 0.842
The half-width is t_{/2, n-1} * s / n = 2.093 * (1.) = 2.093 * (1..472) = 2.093 *
0.4025 = 0.842. Options B, C, D are identical except for wording; A is the numeric
value. The question is flawed but the intended correct answer is the numeric half-width.
Page 3
, 5. In a simulation experiment, the analyst uses a 2^k factorial design to study the
effects of three factors: arrival rate (A), service rate (B), and number of servers (C).
The estimated main effects are: A = 2.3, B = 1.5, C = 0.8. The interaction effects are:
AB = 0.6, AC = 0.2, BC = 0.1, ABC = 0.05. Which of the following interpretations is
correct?
A. Factor A has the largest impact on the response, and there is a strong interaction between
A and B.
B. Factor B has the largest impact because its effect is negative, indicating it reduces the
response.
C. The interaction ABC is negligible, so all two-way interactions can be ignored.
D. Factor C has the smallest main effect, and the AB interaction is practically significant
relative to the main effects.
Answer: D. Factor C has the smallest main effect, and the AB interaction is
practically significant relative to the main effects.
The magnitude of main effect A is 2.3, B is 1.5, C is 0.8, so C has the smallest main
effect. The AB interaction (0.6) is about 40% of the B main effect, which is practically
significant. Option A is incorrect because AB (0.6) is not strong compared to A (2.3).
Option B is incorrect because magnitude matters, not sign. Option C is incorrect
because negligible three-way interaction does not imply two-way interactions are
negligible.
6. A simulation model uses a linear congruential generator (LCG) with parameters:
modulus m = 2^31 1, multiplier a = 7^5, and increment c = 0. The generator is used
to produce uniform(0,1) random numbers. Which of the following statements about
this generator is true?
A. The generator has full period because c = 0 and m is prime.
B. The generator is a multiplicative LCG with period m1 when the seed is relatively prime to
m.
C. The generator will fail the spectral test because a is a power of 7.
D. The generator produces numbers with poor uniformity because c = 0.
Answer: B. The generator is a multiplicative LCG with period m1 when the seed is
relatively prime to m.
This is a multiplicative LCG (c=0). With modulus m prime and a a primitive root
modulo m, the period is m-1. Here, m = 2^31-1 is a Mersenne prime, and 7^5 is a
known primitive root, so period = m-1. Option A is incorrect because full period for
multiplicative LCG is m-1, not m. Option C is not necessarily true; spectral test
depends on a. Option D is false; uniformity can still be good.
Page 4
