ISYE 6644 - Final prep QUESTIONS &
ANSWERS CORRECT DETAILED
ASWERS (VERIFIED ANSWERS)
ALREADY GRADED A+ BAND NEW!!!
• In the above problem, suppose that we take the necessary observations and we
come up with the following sample means: X ¯ 1 = 7.6, X ¯ 2 = 11.1, and X ¯ 3 =
3.6. What do we do? - ✔️✔️Pick population 2 and say that we are right with
probability at least 95%
• 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 ratio of the highest-to-second-highest preference
probabilities happens to be at least θ ⋆ = 1.4. If we use procedure M B E M, then
the corresponding table in the notes (with k = 3) tells us to take 126 samples
(taste tests). Suppose we take those samples sequentially and after 100 have
been taken it turns out that 65 people prefer Coke, 25 love Pepsi, and 10 like Dr.
Pepper. What to do? - ✔️✔️Stop the test now and declare with confidence of at
least 90% that Coke is the most-preferred.
• 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?
• Find the inventory policy having the largest profit.
• Find the drug giving the best chance of a cure.
• Find the maintenance policy having the lowest failure probability.
• 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!
ANSWERS CORRECT DETAILED
ASWERS (VERIFIED ANSWERS)
ALREADY GRADED A+ BAND NEW!!!
• In the above problem, suppose that we take the necessary observations and we
come up with the following sample means: X ¯ 1 = 7.6, X ¯ 2 = 11.1, and X ¯ 3 =
3.6. What do we do? - ✔️✔️Pick population 2 and say that we are right with
probability at least 95%
• 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 ratio of the highest-to-second-highest preference
probabilities happens to be at least θ ⋆ = 1.4. If we use procedure M B E M, then
the corresponding table in the notes (with k = 3) tells us to take 126 samples
(taste tests). Suppose we take those samples sequentially and after 100 have
been taken it turns out that 65 people prefer Coke, 25 love Pepsi, and 10 like Dr.
Pepper. What to do? - ✔️✔️Stop the test now and declare with confidence of at
least 90% that Coke is the most-preferred.
• 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?
• Find the inventory policy having the largest profit.
• Find the drug giving the best chance of a cure.
• Find the maintenance policy having the lowest failure probability.
• 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!
