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Which of the following is a disadvantage of pre-control charts?
a. They do not provide information on how to reduce variability in a
process.
b. They cannot determine if a product being produced is centered between
the tolerances during initial operation setup.
c. They are difficult to interpret.
d. They can be used for processes with a capability ratio less than 1. correct answers (A)
Pre-control charts do not provide information on how variability can be reduced or how to bring
a process into control. They should only be used for processes with a capability ration greater
than one. Poor capability in a pre-control chart will indicate that assignable causes are present
when in fact there are no assignable causes of variation. Small sample sizes in a pre-control chart
will reduce the cart's ability to detect moderate to large shifts. Pre-control charts are useful in
initial setup operations to determine whether a process is centered between the tolerances.
Which of the following is considered attribute data?
a. Customer wait time
b. Number of filing errors
c. Costs of processing applications
d. Thickness of a component correct answers (B)
Attribute data is the term used to describe discrete data in quality control. Wait time, processing
costs, and thickness can each be measured on a continuous scale. The number of filing errors can
only take on a countable set of numbers, and is considered discrete, or attribute, data.
A population. has a distribution with a mean 24 and standard deviation 5.5. What is the
approximate standard deviation of the sampling distribution of the sample mean if random
samples of size 32 are taken?
a. 5.5
b . 5.5/32
c. 5.5/√24
d . 5.5/√32 correct answers (D)
The central limit theorem states that if the sample size n is sufficiently large, then the sample
mean x̄ follows approximately a normal distribution with mean μ↓x̄ = μ and standard deviation
σ↓x̄ = σ/√n.
In this case, μ = 24, σ = 5.5 and n = 32. Therefore, σ↓x̄ = 5.5/√32
A control chart monitoring the viscosity of a product shows that a particular process is out of
control. What should the process operator do?
a. Attempt to fix the problem on their own.
b. Follow the reaction plan detailed in the control plan of the process.
c. Brainstorm to determine the cause of the problem.
d. Nothing; the process will stabilize on its own. correct answers (B)
Control plans include detailed reaction plans that should be followed when the control method
detects a problem in the process. The reaction plan details the steps the operator should take
when the process has a problem .
,An x̄ and R chart was prepared for an operation using 25 samples with four pieces in each
sample. x̅̅ was found to be 26.75 and R¯ was 8.10. During production, a sample of four was
taken and the pieces measured 20, 29, 40, and 25. At the time this sample was taken
a. both the average and range were within the control limits.
b. neither the average nor range were within the control limits.
c. only the average was outside the control limits.
d. only the range was outside the control limits.
(R¯ is R with a bar on top) correct answers (D)
https://docs.google.com/document/d/1n4TBe4uMD4IjlaTu0g31oHdZweuecVrXqgHt2ClUdck/
edit?usp=sharing
Suppose that the p-value of a hypothesis test on μ1 - μ2 is 0.23. What conclusions can be made
(use significance level 10%)?
a. Reject Ho, conclude that the two means are the same.
b. Reject Ho, conclude that the two means are not the same.
c. Do not reject Ho, Conclude that the two means are the same.
process.
d. Do not reject Ho, Conclude that the two means are not the same. correct answers (C)
𝛼 = 0.10 and p-value = 0.23. Using the p-value approach to hypothesis testing, if the p-value < 𝛼,
we do not reject Ho. Since 0.23 > 0.10, we do not reject Ho and conclude that the two means are
the same.
Which phase of the corrective action cycle helps prevent problem backsliding?
a. Problem identification
b. Correction
c. Recurrence control
d. Effectiveness assessment correct answers (C)
In the problem identification phase, the team identifies sources for improvement and develops a
clear problem statement. In the correction phase, the team develops feasible solutions to the
problem and recommends the best choice to implement. In the recurrence control phase, the team
standardizes the solution to ensure that the problem does not reoccur and prevent backsliding.
Finally, in the effectiveness assessment phase, the team continues monitoring the process to
identify additional opportunities for improvement.
A team were investigated the number of patient falls in a hospital. Fifty-six patients were
randomly selected. Out of the 56 patients, there were six recorded patient falls. Using this
information, construct a 90% confidence interval on the true proportion of patient falls in this
hospital.
a. (-0.4016, 0.6158)
b. (0, 0.6158)
c. (0.0006, 0.2136)
d. (0.0391, 0.1751) correct answers (D)
In this problem, a "success" is a patient fall. Therefore, x = 6 and n = 56.
, We are 90% confident that the true proportion of patient falls in the hospital is between 3.91%
and 17.5l%.
A gage R&R study was preformed for a process with 10 parts, tow operators, and three
replicates. The x̄ chart below displays information about the gage
capability. What conclusions can be drawn from this control chart?
chart:
https://docs.google.com/document/d/1BXztHByUWC7ZOGKGoOzBHALdvv3Oy7V0zONooR
HJzgM/edit?usp=sharing
a. The gage is capable of distinguishing between parts.
b. There is a significant difference between operators.
c. The chart reflects variability related to gage reproducibility.
d. The gage is not capable of distinguishing between parts. correct answers (D) The x̄ control
chart reflects within-sample variability, which is related to gage repeatability. If the gage is
capable, then it should be able to distinguish between parts. Therefore, we would expect many of
the points to plot outside the control limits. In this case, most of the points are within the control
limits; this indicates that the gage cannot distinguish between parts.
Find the probability that Z, the standard normal distribution, lies between -1.02 and 0.58.
a. 0.5651
b. 0.1539
c. 0.7190
d. 0.4349 correct answers (A)
From the properties of the cumulative distribution function,
P(a < Z <b) = P(Z < b) - P(Z < a). Therefore, using a standard normal table,
P(-1.02 < Z < 0.58) = P(Z < 0.58) - P(Z < -1.02) = 0.7190- 0.1539 = 0.5651.
https://docs.google.com/document/d/
1XFypHry8N1U6pZpy8pMo2qbvTfTlku5dOCo4VqySry4/edit?usp=sharing
The date of a customer's visit to a store is on which measurement scale?
a. Nominal
b. Ordinal
c. Interval
d. Ratio correct answers (C)
A date is on an interval scale. There are meaningful differences between two dates, but there is
no absolute zero. Dates can be added or subtracted. For example, you can calculate the number
of days between two dates by subtracting them. However, you cannot meaningfully multiply or
divide two dates.
What is a benefit of implementing standardized work in an organization?
a. Reductions in process variation
b. More consistent products
c. Simplified downstream activities
d. All of the above correct answers (D)
Which of the following is a disadvantage of pre-control charts?
a. They do not provide information on how to reduce variability in a
process.
b. They cannot determine if a product being produced is centered between
the tolerances during initial operation setup.
c. They are difficult to interpret.
d. They can be used for processes with a capability ratio less than 1. correct answers (A)
Pre-control charts do not provide information on how variability can be reduced or how to bring
a process into control. They should only be used for processes with a capability ration greater
than one. Poor capability in a pre-control chart will indicate that assignable causes are present
when in fact there are no assignable causes of variation. Small sample sizes in a pre-control chart
will reduce the cart's ability to detect moderate to large shifts. Pre-control charts are useful in
initial setup operations to determine whether a process is centered between the tolerances.
Which of the following is considered attribute data?
a. Customer wait time
b. Number of filing errors
c. Costs of processing applications
d. Thickness of a component correct answers (B)
Attribute data is the term used to describe discrete data in quality control. Wait time, processing
costs, and thickness can each be measured on a continuous scale. The number of filing errors can
only take on a countable set of numbers, and is considered discrete, or attribute, data.
A population. has a distribution with a mean 24 and standard deviation 5.5. What is the
approximate standard deviation of the sampling distribution of the sample mean if random
samples of size 32 are taken?
a. 5.5
b . 5.5/32
c. 5.5/√24
d . 5.5/√32 correct answers (D)
The central limit theorem states that if the sample size n is sufficiently large, then the sample
mean x̄ follows approximately a normal distribution with mean μ↓x̄ = μ and standard deviation
σ↓x̄ = σ/√n.
In this case, μ = 24, σ = 5.5 and n = 32. Therefore, σ↓x̄ = 5.5/√32
A control chart monitoring the viscosity of a product shows that a particular process is out of
control. What should the process operator do?
a. Attempt to fix the problem on their own.
b. Follow the reaction plan detailed in the control plan of the process.
c. Brainstorm to determine the cause of the problem.
d. Nothing; the process will stabilize on its own. correct answers (B)
Control plans include detailed reaction plans that should be followed when the control method
detects a problem in the process. The reaction plan details the steps the operator should take
when the process has a problem .
,An x̄ and R chart was prepared for an operation using 25 samples with four pieces in each
sample. x̅̅ was found to be 26.75 and R¯ was 8.10. During production, a sample of four was
taken and the pieces measured 20, 29, 40, and 25. At the time this sample was taken
a. both the average and range were within the control limits.
b. neither the average nor range were within the control limits.
c. only the average was outside the control limits.
d. only the range was outside the control limits.
(R¯ is R with a bar on top) correct answers (D)
https://docs.google.com/document/d/1n4TBe4uMD4IjlaTu0g31oHdZweuecVrXqgHt2ClUdck/
edit?usp=sharing
Suppose that the p-value of a hypothesis test on μ1 - μ2 is 0.23. What conclusions can be made
(use significance level 10%)?
a. Reject Ho, conclude that the two means are the same.
b. Reject Ho, conclude that the two means are not the same.
c. Do not reject Ho, Conclude that the two means are the same.
process.
d. Do not reject Ho, Conclude that the two means are not the same. correct answers (C)
𝛼 = 0.10 and p-value = 0.23. Using the p-value approach to hypothesis testing, if the p-value < 𝛼,
we do not reject Ho. Since 0.23 > 0.10, we do not reject Ho and conclude that the two means are
the same.
Which phase of the corrective action cycle helps prevent problem backsliding?
a. Problem identification
b. Correction
c. Recurrence control
d. Effectiveness assessment correct answers (C)
In the problem identification phase, the team identifies sources for improvement and develops a
clear problem statement. In the correction phase, the team develops feasible solutions to the
problem and recommends the best choice to implement. In the recurrence control phase, the team
standardizes the solution to ensure that the problem does not reoccur and prevent backsliding.
Finally, in the effectiveness assessment phase, the team continues monitoring the process to
identify additional opportunities for improvement.
A team were investigated the number of patient falls in a hospital. Fifty-six patients were
randomly selected. Out of the 56 patients, there were six recorded patient falls. Using this
information, construct a 90% confidence interval on the true proportion of patient falls in this
hospital.
a. (-0.4016, 0.6158)
b. (0, 0.6158)
c. (0.0006, 0.2136)
d. (0.0391, 0.1751) correct answers (D)
In this problem, a "success" is a patient fall. Therefore, x = 6 and n = 56.
, We are 90% confident that the true proportion of patient falls in the hospital is between 3.91%
and 17.5l%.
A gage R&R study was preformed for a process with 10 parts, tow operators, and three
replicates. The x̄ chart below displays information about the gage
capability. What conclusions can be drawn from this control chart?
chart:
https://docs.google.com/document/d/1BXztHByUWC7ZOGKGoOzBHALdvv3Oy7V0zONooR
HJzgM/edit?usp=sharing
a. The gage is capable of distinguishing between parts.
b. There is a significant difference between operators.
c. The chart reflects variability related to gage reproducibility.
d. The gage is not capable of distinguishing between parts. correct answers (D) The x̄ control
chart reflects within-sample variability, which is related to gage repeatability. If the gage is
capable, then it should be able to distinguish between parts. Therefore, we would expect many of
the points to plot outside the control limits. In this case, most of the points are within the control
limits; this indicates that the gage cannot distinguish between parts.
Find the probability that Z, the standard normal distribution, lies between -1.02 and 0.58.
a. 0.5651
b. 0.1539
c. 0.7190
d. 0.4349 correct answers (A)
From the properties of the cumulative distribution function,
P(a < Z <b) = P(Z < b) - P(Z < a). Therefore, using a standard normal table,
P(-1.02 < Z < 0.58) = P(Z < 0.58) - P(Z < -1.02) = 0.7190- 0.1539 = 0.5651.
https://docs.google.com/document/d/
1XFypHry8N1U6pZpy8pMo2qbvTfTlku5dOCo4VqySry4/edit?usp=sharing
The date of a customer's visit to a store is on which measurement scale?
a. Nominal
b. Ordinal
c. Interval
d. Ratio correct answers (C)
A date is on an interval scale. There are meaningful differences between two dates, but there is
no absolute zero. Dates can be added or subtracted. For example, you can calculate the number
of days between two dates by subtracting them. However, you cannot meaningfully multiply or
divide two dates.
What is a benefit of implementing standardized work in an organization?
a. Reductions in process variation
b. More consistent products
c. Simplified downstream activities
d. All of the above correct answers (D)
