Deck 22: Business Statistics

Question 1

Identify the appropriate control chart for attributes data.
A manufacturer of a particular grade of copper tubing collects data on the number of
Flaws occurring in 500 foot coils. Suppose they sample a total of 40 coils to initiate
Control charting. The average number of defects per coil is 2.5. The appropriate control
Chart for these data is the

A) R chart.
B) c chart.
C) x-bar and R chart.
D) p chart.
E) ARL chart.

Answer 1

B

Question 2

Estimate the process standard deviation.
An automatic filling process is used to dispense hand sanitizer into small purse size
Bottles. The target weight is 75 ml. The company has initiated control charting to
Stabilize and improve the automatic filling process. For each of twenty-five samples
Consisting of four bottles, the contents were measured and the mean weight and range
Were determined. The average of the means across all samples was found to be 72.5 ml.
And the average range was 2.75 ml. The estimate of the process standard deviation is

A) 2.75 ml
B) 2.44 ml
C) 1.88 ml
D) 1.34 ml
E) None of the above

Answer 2

D

Question 3

Create p-charts.
An importer of decorative ceramic tile samples 50 tiles each day from incoming
Shipments. Some tiles are cracked or broken before or during transit, rendering them
Useless scrap. Sampling from incoming shipments for 30 days reveals that a total of 250
Tiles are cracked or broken. The centerline on the p chart for these data is

A) 0.250
B) 1.83.
C) 2.5.
D) 0.167.
E) 6.1.

Answer 3

D

Question 4

Create X-bar and R charts.
A company that manufactures health food snacks produces low sodium rice chips. To
Monitor the process for sodium levels, chips are selected periodically and the amount of
Sodium (mg) measured. For each of thirty samples consisting of 8 chips, the mean and
Range in sodium content is determined. The average of the means across all samples is 55
Mg and the average range is 2.2 mg. The lower and upper control limits for the R chart
Are

A) 0.2992 and 4.1008 mg.
B) 0 and 4.4088 mg.
C) 0.136 and 1.864 mg.
D) 2.1999 and 30.152 mg.
E) 0.2493 and 3.4167 mg.

Question 5

Create p-charts.
In order to achieve higher levels of customer satisfaction, a company initiates
Monitoring the complaint resolution process of its customer service representatives. As a
First step, the company decides to collect data on the number of unanswered calls out of
The first 250 incoming calls to its call center made each day. At the end of monitoring 25
Days, it was found that a total of 500 incoming calls went unanswered. The control limits
For the p-chart of these data are

A) 0.029 and 0.131
B) 0 and 0.304
C) 0.066 and 0.094
D) 0.048 and 0.112
E) None of the above

Question 6

Create X-bar and R charts.
An automatic filling process is used to dispense hand sanitizer into small purse size
Bottles. The target weight is 75 ml. The company has initiated control charting to
Stabilize and improve the automatic filling process. For each of twenty-five samples
Consisting of four bottles, the contents were measured and the mean weight and range
Were determined. The average of the means across all samples was found to be 72.5 ml.
And the average range was 2.75 ml. The control limits for the X-bar chart are

A) 68.48 and 76.52 ml
B) 71.16 and 73.84 ml
C) 70.49 and 74.51 ml
D) 72 and 73 ml
E) None of the above

Question 7

Understand the purpose of control charts.
Which of the following statements is false regarding control charts?

A) If we view using a control chart as a graphical hypothesis test, the null hypothesis is that the process has not changed.
B) A type I error in control charting results in an unnecessary adjustment to the process.
C) A type II error in control charting results in an unnecessary adjustment to the process.
D) A process within which special cause variation is present is said to be out of control.
E) A process which exhibits only common cause variation is said to be in control.

Question 8

Identify the appropriate control chart for measured data.
A paper products manufacturer coats paper with a thin film of wax. To initiate control
Charting, data are collected on the thickness of the coating (measured in mm) by taking
Twenty-five samples each of size five. The appropriate control chart for these data is the

A) c chart.
B) p chart.
C) Cp index.
D) x-bar and R chart.
E) ARL chart.

Question 9

Compute process capability indices.

-By design, a required dimension on a part is 0.575 inches plus or minus 0.008 inches. Assume that the process producing this part is stable with a mean of $0.579$ inches and standard deviation of $0.002$ inches. What is the $C _ { p }$ index?

A) 1.33
B) 2.00
C) 0.67
D) 1.00
E) None of the above

Question 10

Compute process capability indices.

-Machine oil is used by clothing manufacturers to lubricate and protect sewing
Machines. A company that produces machine oil must ensure that the viscosity of its product meets customer requirements. Consequently, the viscosity of every batch of oil produced is measured. Suppose that the process mean is $101 \mathrm { cP }$ and the process standard deviation is $1.50 \mathrm { cP }$ . What is the $\mathrm { C } _ { \mathrm { pk } }$ index if the customer specifications require viscosity of the machine oil to be $100 \mathrm { cP } \pm 4.5 \mathrm { cP }$ ?

A) 1.0
B) 1.22
C) 0.78
D) 1.67
E) None of the above

Question 11

Create c-charts.
A manufacturer of a particular grade of copper tubing collects data on the number of
Flaws occurring in 500 foot coils. Suppose they sample a total of 40 coils to initiate
Control charting. The average number of defects per coil is 2.5. The lower and upper
Control limits for the appropriate control chart for these data are

A) 0 and 7.24.
B) 0 and 5.66.
C) 2.24 and 7.24.
D) 2.24 and 4.08.
E) none of the above.

Question 12

Create X-bar and R charts.
An automatic filling process is used to dispense hand sanitizer into small purse size
Bottles. The target weight is 75 ml. The company has initiated control charting to
Stabilize and improve the automatic filling process. For each of twenty-five samples
Consisting of four bottles, the contents were measured and the mean weight and range
Were determined. The average of the means across all samples was found to be 72.5 ml.
And the average range was 2.75 ml. The control limits for the R chart are

A) 0 and 4.3566 ml
B) 0 and 6.2755 ml
C) 0 and 2.8875 ml
D) 2.00 and 3.50 ml
E) None of the above

Question 13

Identify the appropriate control chart for attributes data.
A producer of specialty products uses a variety of natural and man-made materials to
Make unique countertops for kitchens and baths. One product line mixes concrete and
Natural river stone to make countertops that are polished to a high shine revealing unique
Patterns. Occasionally coarse sand will result in undesirable pitting and rough spots on
Surfaces. Consequently, as part of its quality control efforts, 8 by 4 foot polished slabs
Are checked periodically for imperfections. For each slab inspected the number of
Imperfections (pits, rough spots, etc.) is recorded. What type of control chart should be
Used for these data?

A) Individuals chart
B) P-chart
C) C-chart
D) X-bar and R charts
E) ARL chart

Question 14

Create X-bar and R charts.
A company that manufactures health food snacks produces low sodium rice chips. To
Monitor the process for sodium levels, chips are selected periodically and the amount of
Sodium (mg) measured. For each of thirty samples consisting of 8 chips, the mean and
Range in sodium content is determined. The average of the means across all samples is 55
Mg and the average range is 2.2 mg. The lower and upper control limits for the x-bar
Chart are

A) 52.67 and 57.33 mg.
B) 51.15 and 58.85 mg.
C) 54.18 and 55.82 mg.
D) 48.89 and 57.61 mg.
E) 37.84 and 72.16 mg.

Question 15

Create c-charts.
A producer of specialty products uses a variety of natural and man-made materials to
Make unique countertops for kitchens and baths. One product line mixes concrete and
Natural river stone to make countertops that are polished to a high shine revealing unique
Patterns. Occasionally coarse sand will result in undesirable pitting and rough spots on
Surfaces. Consequently, as part of its quality control efforts, 8 by 4 foot polished slabs
Are checked periodically for imperfections. For each slab inspected the number of
Imperfections (pits, rough spots, etc.) is recorded. If the average number of imperfections
Per 8 by 4 foot polished slab is 2.6, the control limits for the appropriate control chart are

A) 0 and 7.44
B) 0.98 and 4.21
C) 0 and 9.89
D) 1.24 and 3.96
E) None of the above

Question 16

Distinguish between specification and control limits.
By design, a required dimension on a part is 0.575 inches plus or minus 0.008 inches.
Assume that the process producing this part is stable with a mean of 0.579 inches and
Standard deviation of 0.002 inches. The specification limits for this part are

A) 0.554 to 0.596 inches.
B) 0.567 to 0.583 inches.
C) 0.576 to 0.598 inches.
D) 0.572 to 0.584 inches.
E) 0.575 to 0.578 inches.

Question 17

Distinguish between specification and control limits.
Machine oil is used by clothing manufacturers to lubricate and protect sewing
Machines. A company that produces machine oil must ensure that the viscosity of its
Product meets customer requirements. Consequently, the viscosity of every batch of oil
Produced is measured. Suppose that the process mean is 101 cP and the process standard
Deviation is 1.50 cP. What are the limits for a runs chart to be used to see that the process
Remains control?

Question 18

Understand the purpose of control charts.
Machine oil is used by clothing manufacturers to lubricate and protect sewing
Machines. A company that produces machine oil must ensure that the viscosity of its
Product meets customer requirements. Consequently, the viscosity of every batch of oil
Produced is measured. Suppose that the process mean is 101 cP and the process standard
Deviation is 1.50 cP. What type of chart should be used to ensure the process remains in
Control?

A) p-chart
B) c-chart
C) R-chart
D) Individuals chart
E) ARL chart

Question 19

Create p-charts.
An importer of decorative ceramic tile samples 50 tiles each day from incoming
Shipments. Some tiles are cracked or broken before or during transit, rendering them
Useless scrap. Sampling from incoming shipments for 30 days reveals that a total of 250
Tiles are cracked or broken. The lower and upper control limits on the p chart for these
Data are

A) 0.067 and 0.299.
B) 0.157 and 0.177.
C) 0 and 0.299.
D) 1.314 and 10.886.
E) 0.009 and 0.325.

Question 20

Estimate the process standard deviation.
A company that manufactures health food snacks produces low sodium rice chips. To
Monitor the process for sodium levels, chips are selected periodically and the amount of
Sodium (mg) measured. For each of thirty samples consisting of 8 chips, the mean and
Range in sodium content is determined. The average of the means across all samples is 55
Mg and the average range is 2.2 mg. The estimated process standard deviation (σˆ ) is

A) 0.773 mg.
B) 2.683 mg.
C) 0.073 mg.
D) 16.176 mg.
E) 1.833 mg.