Question 1

SCENARIO 18-1
A local newspaper has 10 delivery boys who each deliver the morning paper to 50 customers every
day. The owner decides to record the number of papers delivered on time for a 10-day period for one
of the delivery boys and construct a p chart to see whether the percentage is too erratic.
Number of Papers $$\begin{array}{l}
\begin{array} { r r } 
&\text { Number of Papers }\
 \underline{ \text { Day } }  &  \underline{ \text { Delivered} } \ 
1 & 46 \
2 & 45 \
3 & 46 \
4 & 45 \
5 & 43 \
6 & 48 \
7 & 46 \
8 & 49 \
9 & 48 \
10 & 47
\end{array}
\end{array}$$
-Referring to Scenario 18-1, what is the numerical value of the upper control limit for the p chart?
A) 0.926
B) 0.961
C) 0.979
D) 1.037

Accepted Answer

D

Question 2

Once the control limits are set for a control chart, one attempts to
A) discern patterns that might exist in values over time.
B) determine whether any points fall outside the control limits.
C) Both of the above.
D) None of the above.

Accepted Answer

Once the control limits are set for a control chart, one attempts to discern patterns that might exist in values over time and determine whether any points fall outside the control limits. Therefore, both options A and B are correct.

Question 3

SCENARIO 18-3
A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a
batch of light bulbs is too erratic. Accordingly, the analyst randomly surveys 10 production periods
each day for 14 days and records the sample mean and range for each day. $\begin{array}{ccc}
 \underline{\text { Day } }& \underline{\bar{X} \text { (in minutes) }} & \underline{\text {R}}\
1 & 58.5 & 5.1 \
2 & 47.6 & 7.8 \
3 & 64.3 & 6.1 \
4 & 60.6 & 5.7 \
5 & 63.7 & 6.2 \
6 & 57.5 & 6.0 \
7 & 55.0 & 5.4 \
8 & 54.9 & 6.1 \
9 & 55.0 & 5.9 \
10 & 62.7 & 5.0 \
11 & 61.9 & 7.1 \
12 & 60.0 & 6.5 \
13 & 58.3 & 5.9 \
14 & 52.0 & 5.2
\end{array}$

-Referring to Scenario 18-3, suppose the analyst constructs an R chart to see if the variability in production times is in-control. What is the center line of this R chart?
A) 4.8
B) 6.0
C) 6.9
D) 7.1

Accepted Answer

The center line of an R chart is the average of the sample ranges. Calculating the average of the given ranges: (5.1 + 7.8 + 6.1 + 5.7 + 6.2 + 6.0 + 5.4 + 6.1 + 5.9 + 5.0 + 7.1 + 6.5 + 5.9 + 5.2) / 14 = 6.0.

Question 4

One of the morals of the red bead experiment is:
A) variation is part of the process.
B) only management can change the system.
C) it is the system that primarily determines performance.
D) All of the above.

Accepted Answer

The red bead experiment demonstrates that variation is part of the process, and that the system primarily determines performance. Additionally, the experiment shows that only management can change the system. Therefore, all of the above options are correct as morals of the experiment.

Question 5

Variation signaled by individual fluctuations or patterns in the data is called
A) special or assignable causes.
B) common or chance causes.
C) explained variation.
D) the standard deviation.

Accepted Answer

Individual fluctuations or patterns in the data are known as special or assignable causes of variation. These causes can be identified and eliminated to improve the overall process. Common or chance causes of variation, on the other hand, are inherent to the process and cannot be eliminated. Explained variation refers to the portion of total variation that can be attributed to a specific factor, while the standard deviation is a measure of the spread of the data.

Question 6

Which of the following situations suggests a process that appears to be operating out of statistical control?
A) A control chart with a series of consecutive points that are above the center line and a series of consecutive points that are below the center line.
B) A control chart in which points fall outside the lower control limit.
C) A control chart in which several points fall outside the upper control limit.
D) All of the above.

Accepted Answer

All the described situations suggest a process that is operating out of statistical control. Consecutive points consistently above or below the center line, points falling outside the lower control limit, and several points outside the upper control limit all indicate potential issues with process stability or control.

Question 7

SCENARIO 18-1
A local newspaper has 10 delivery boys who each deliver the morning paper to 50 customers every
day. The owner decides to record the number of papers delivered on time for a 10-day period for one
of the delivery boys and construct a p chart to see whether the percentage is too erratic.
Number of Papers $$\begin{array}{l}
\begin{array} { r r } 
&\text { Number of Papers }\
 \underline{ \text { Day } }  &  \underline{ \text { Delivered} } \ 
1 & 46 \
2 & 45 \
3 & 46 \
4 & 45 \
5 & 43 \
6 & 48 \
7 & 46 \
8 & 49 \
9 & 48 \
10 & 47
\end{array}
\end{array}$$
-Referring to Scenario 18-1, what is the numerical value of the center line for the p chart?
A) 0.926
B) 0.911
C) 0.885
D) 0.500

Accepted Answer

The center line for a p chart is the average proportion of successes. Here, the total number of papers delivered on time is 463 out of 500 (10 days * 50 papers), so the center line is 463/500 = 0.926.

Question 8

SCENARIO 18-1
A local newspaper has 10 delivery boys who each deliver the morning paper to 50 customers every
day. The owner decides to record the number of papers delivered on time for a 10-day period for one
of the delivery boys and construct a p chart to see whether the percentage is too erratic.
Number of Papers $$\begin{array}{l}
\begin{array} { r r } 
&\text { Number of Papers }\
 \underline{ \text { Day } }  &  \underline{ \text { Delivered} } \ 
1 & 46 \
2 & 45 \
3 & 46 \
4 & 45 \
5 & 43 \
6 & 48 \
7 & 46 \
8 & 49 \
9 & 48 \
10 & 47
\end{array}
\end{array}$$
-Referring to Scenario 18-1, what is the numerical value of the lower control limit for the p chart?
A) 0.920
B) 0.911
C) 0.815
D) 0.798

Accepted Answer

The lower control limit (LCL) for a p chart is calculated using the formula: LCL = p̄ - 3√(p̄(1-p̄)/n), where p̄ is the average proportion of successes and n is the sample size. Here, p̄ = (46+45+46+45+43+48+46+49+48+47)/(10*50) = 0.463, and n = 50. Calculating LCL gives approximately 0.815.

Question 9

The principal focus of the control chart is the attempt to separate special or assignable causes of variation from common causes of variation. Which causes of variation can be reduced only by
Changing the system?
A) Special or assignable causes
B) Common causes
C) Total causes
D) None of the above

Accepted Answer

Common causes of variation are inherent in the system and can only be reduced by changing the system itself.

Question 10

SCENARIO 18-2
A political pollster randomly selects a sample of 100 voters each day for 8 successive days and asks
how many will vote for the incumbent. The pollster wishes to construct a p chart to see if the
percentage favoring the incumbent candidate is too erratic. $$\begin{array} { c c } 
\begin{array} { c } 
\text { Sample } \
\underline{\text { (Day) }}
\end{array} & \begin{array} { c } 
\text { Number Favoring } \
\underline{\text { Incumbent Candidate }}
\end{array} \
 1 & 57 \
2 & 57 \
3 & 53 \
4 & 51 \
5 & 55 \
6 & 60 \
7 & 56 \
8 & 59
\end{array}$$
-Referring to Scenario 18-2, which expression best characterizes the p chart?
A) In-control
B) Increasing trend
C) Decreasing trend
D) Individual outliers

Accepted Answer

The p chart is in control because all the points are within the control limits.

Question 11

The control chart
A) focuses on the time dimension of a system.
B) captures the natural variability in the system.
C) can be used for categorical, discrete, or continuous variables.
D) All of the above.

Accepted Answer

The control chart focuses on the time dimension of a system, captures the natural variability in the system, and can be used for categorical, discrete, or continuous variables. Therefore, all the options A, B, and C are correct, making D the best choice.

Question 12

SCENARIO 18-1
A local newspaper has 10 delivery boys who each deliver the morning paper to 50 customers every
day. The owner decides to record the number of papers delivered on time for a 10-day period for one
of the delivery boys and construct a p chart to see whether the percentage is too erratic.
Number of Papers $$\begin{array}{l}
\begin{array} { r r } 
&\text { Number of Papers }\
 \underline{ \text { Day } }  &  \underline{ \text { Delivered} } \ 
1 & 46 \
2 & 45 \
3 & 46 \
4 & 45 \
5 & 43 \
6 & 48 \
7 & 46 \
8 & 49 \
9 & 48 \
10 & 47
\end{array}
\end{array}$$
-Referring to Scenario 18-1, which expression best characterizes the p chart?
A) Cycles
B) Increasing trend
C) In-control
D) Individual outliers

Accepted Answer

The data shows a consistent pattern with no significant deviations, indicating the process is in control.

Question 13

Which of the following situations suggests a process that appears to be operating in a state of statistical control?
A) A control chart with a series of consecutive points that are above the center line and a series of consecutive points that are below the center line.
B) A control chart in which no points fall outside either the upper control limit or the lower control limit and no patterns are present.
C) A control chart in which several points fall outside the upper control limit.
D) All of the above.

Accepted Answer

A control chart in which no points fall outside either the upper control limit or the lower control limit and no patterns are present suggests that the process is operating in a state of statistical control, meaning that the process is stable and predictable. This indicates that the process is producing consistent results and can be used to make decisions and improve performance. Option A indicates a pattern of instability, while option C suggests that the process is out of control.

Question 14

SCENARIO 18-3
A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a
batch of light bulbs is too erratic. Accordingly, the analyst randomly surveys 10 production periods
each day for 14 days and records the sample mean and range for each day. $\begin{array}{ccc}
 \underline{\text { Day } }& \underline{\bar{X} \text { (in minutes) }} & \underline{\text {R}}\
1 & 58.5 & 5.1 \
2 & 47.6 & 7.8 \
3 & 64.3 & 6.1 \
4 & 60.6 & 5.7 \
5 & 63.7 & 6.2 \
6 & 57.5 & 6.0 \
7 & 55.0 & 5.4 \
8 & 54.9 & 6.1 \
9 & 55.0 & 5.9 \
10 & 62.7 & 5.0 \
11 & 61.9 & 7.1 \
12 & 60.0 & 6.5 \
13 & 58.3 & 5.9 \
14 & 52.0 & 5.2
\end{array}$

-Referring to Scenario 18-3, suppose the analyst constructs an R chart to see if the variability in production times is in-control. What is the upper control limit for this R chart?
A) 10.66
B) 9.37
C) 7.98
D) 6.34

Accepted Answer

The answer of SCENARIO 18-3
A quality control analyst for a...

Question 15

SCENARIO 18-2
A political pollster randomly selects a sample of 100 voters each day for 8 successive days and asks
how many will vote for the incumbent. The pollster wishes to construct a p chart to see if the
percentage favoring the incumbent candidate is too erratic. $$\begin{array} { c c } 
\begin{array} { c } 
\text { Sample } \
\underline{\text { (Day) }}
\end{array} & \begin{array} { c } 
\text { Number Favoring } \
\underline{\text { Incumbent Candidate }}
\end{array} \
 1 & 57 \
2 & 57 \
3 & 53 \
4 & 51 \
5 & 55 \
6 & 60 \
7 & 56 \
8 & 59
\end{array}$$
-Referring to Scenario 18-2, what is the numerical value of the upper control limit for the p chart?
A) 0.92
B) 0.89
C) 0.71
D) 0.62

Accepted Answer

The answer of SCENARIO 18-2
A political pollster randomly selects a...

Question 16

SCENARIO 18-2
A political pollster randomly selects a sample of 100 voters each day for 8 successive days and asks
how many will vote for the incumbent. The pollster wishes to construct a p chart to see if the
percentage favoring the incumbent candidate is too erratic. $$\begin{array} { c c } 
\begin{array} { c } 
\text { Sample } \
\underline{\text { (Day) }}
\end{array} & \begin{array} { c } 
\text { Number Favoring } \
\underline{\text { Incumbent Candidate }}
\end{array} \
 1 & 57 \
2 & 57 \
3 & 53 \
4 & 51 \
5 & 55 \
6 & 60 \
7 & 56 \
8 & 59
\end{array}$$
-Referring to Scenario 18-2, what is the numerical value of the lower control limit for the p chart?
A) 0.37
B) 0.41
C) 0.50
D) 0.71

Accepted Answer

The lower control limit (LCL) for a p chart is calculated using the formula: LCL = p̄ - 3√(p̄(1-p̄)/n), where p̄ is the average proportion and n is the sample size. Here, p̄ = (57+57+53+51+55+60+56+59)/800 = 0.56. Thus, LCL = 0.56 - 3√(0.56(1-0.56)/100) ≈ 0.41.

Question 17

SCENARIO 18-2
A political pollster randomly selects a sample of 100 voters each day for 8 successive days and asks
how many will vote for the incumbent. The pollster wishes to construct a p chart to see if the
percentage favoring the incumbent candidate is too erratic. $$\begin{array} { c c } 
\begin{array} { c } 
\text { Sample } \
\underline{\text { (Day) }}
\end{array} & \begin{array} { c } 
\text { Number Favoring } \
\underline{\text { Incumbent Candidate }}
\end{array} \
 1 & 57 \
2 & 57 \
3 & 53 \
4 & 51 \
5 & 55 \
6 & 60 \
7 & 56 \
8 & 59
\end{array}$$
-Referring to Scenario 18-2, what is the numerical value of the center line for the p chart?
A) 0.53
B) 0.56
C) 0.63
D) 0.66

Accepted Answer

The center line for a p chart is the average proportion of successes. Here, it is the average number of voters favoring the incumbent over the 8 days, which is (57+57+53+51+55+60+56+59)/800 = 0.56.

Question 18

Variation due to the inherent variability in a system of operation is called
A) special or assignable causes.
B) common or chance causes.
C) explained variation.
D) the standard deviation.

Accepted Answer

Common or chance causes refer to the inherent variability in a system of operation that cannot be explained by specific causes. Special or assignable causes, on the other hand, refer to specific factors that cause variations in the system. Explained variation is the variation that can be attributed to specific causes or factors, while the standard deviation is a measure of the spread of data in a set.

Question 19

SCENARIO 18-3
A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a
batch of light bulbs is too erratic. Accordingly, the analyst randomly surveys 10 production periods
each day for 14 days and records the sample mean and range for each day. $\begin{array}{ccc}
 \underline{\text { Day } }& \underline{\bar{X} \text { (in minutes) }} & \underline{\text {R}}\
1 & 58.5 & 5.1 \
2 & 47.6 & 7.8 \
3 & 64.3 & 6.1 \
4 & 60.6 & 5.7 \
5 & 63.7 & 6.2 \
6 & 57.5 & 6.0 \
7 & 55.0 & 5.4 \
8 & 54.9 & 6.1 \
9 & 55.0 & 5.9 \
10 & 62.7 & 5.0 \
11 & 61.9 & 7.1 \
12 & 60.0 & 6.5 \
13 & 58.3 & 5.9 \
14 & 52.0 & 5.2
\end{array}$

-Referring to Scenario 18-3, suppose the analyst constructs an R chart to see if the variability in production times is in-control. What is the lower control limit for this R chart?
A) 4.84
B) 3.37
C) 2.98
D) 1.34

Accepted Answer

The answer of SCENARIO 18-3
A quality control analyst for a...

Question 20

A process is said to be out of control if
A) a point falls above the upper or below the lower control lines.
B) eight or more consecutive points fall above the center line or eight or more consecutive points fall below the center line.
C) Either of the above.
D) None of the above.

Accepted Answer

Both A and B are conditions for a process to be considered out of control, therefore the best choice is C which encompasses both scenarios.

Quiz 18: Statistical Applications in Quality Management

Once the control limits are set for a control chart, one attempts to

One of the morals of the red bead experiment is:

Variation signaled by individual fluctuations or patterns in the data is called

Which of the following situations suggests a process that appears to be operating out of statistical control?

The principal focus of the control chart is the attempt to separate special or assignable causes of variation from common causes of variation. Which causes of variation can be reduced only by Changing the system?

The control chart

Which of the following situations suggests a process that appears to be operating in a state of statistical control?

Variation due to the inherent variability in a system of operation is called

A process is said to be out of control if