Find the estimate of the mean when the process is in control.

Question

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Answer 1

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 19, Problem 16SE

a.

To determine

Find the estimate of the mean when the process is in control.

a.

Expert Solution

Answer to Problem 16SE

The estimate of the mean for the production process that is in control is 95.4.

Explanation of Solution

Calculation:

The means for 20 samples of a production process are provided.

The estimate of the mean for the production process is given below:

μ=∑x¯n=(95.72+95.44+95.40+95.50+95.56+95.72+95.60+95.24+95.46+95.44+95.80+95.22+94.82+95.78+95.18+95.32+95.08+95.22+95.04+95.46)20=1,90820=95.4

Thus, the estimate of the mean for the production process that is in control is 95.4.

b.

To determine

Construct a x¯ control chart for the production process.

b.

Expert Solution

Answer to Problem 16SE

Output obtained using MINITAB software is given below:

Modern Business Statistics with Microsoft Excel (MindTap Course List), Chapter 19, Problem 16SE

Explanation of Solution

Calculation:

Upper control limits for the x¯chart:

UCL=μ+3σn=95.4+30.505=95.4+0.6696=96.07

Lower control limits for the x¯chart:

LCL=μ−3σn=95.4−30.505=95.4−0.6696=94.73

X-bar chart:

Software procedure:

Step-by-step software procedure to obtain the X-bar chart using EXCEL:

Open an EXCEL file.
Enter the observation.
Enter X-double bar in a new cell B1, in cell B2 enter a formula “=Average(A2:A21)”.
Click Enter.
Click on Insert > select Insert Line chart icon.
Click on the chart > select Layout from the Chart Tools.
Select Chart Title > Above Chart.
Enter X-bar Chart in the dialog box.

Thus, the control limits for the x¯ chart are UCL=96.07 and LCL=94.73.

c.

To determine

Explain whether any of the 20 sample means indicate that the process is out of control or not.

c.

Expert Solution

Explanation of Solution

From the x¯ chart, it is observed that all the sample means lie within UCL and LCL.

Thus, the 20 sample means do not indicate that the process was out of control.

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Answer 2

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 19, Problem 16SE

a.

To determine

Find the estimate of the mean when the process is in control.

a.

Expert Solution

Answer to Problem 16SE

The estimate of the mean for the production process that is in control is 95.4.

Explanation of Solution

Calculation:

The means for 20 samples of a production process are provided.

The estimate of the mean for the production process is given below:

μ=∑x¯n=(95.72+95.44+95.40+95.50+95.56+95.72+95.60+95.24+95.46+95.44+95.80+95.22+94.82+95.78+95.18+95.32+95.08+95.22+95.04+95.46)20=1,90820=95.4

Thus, the estimate of the mean for the production process that is in control is 95.4.

b.

To determine

Construct a x¯ control chart for the production process.

b.

Expert Solution

Answer to Problem 16SE

Output obtained using MINITAB software is given below:

Modern Business Statistics with Microsoft Excel (MindTap Course List), Chapter 19, Problem 16SE

Explanation of Solution

Calculation:

Upper control limits for the x¯chart:

UCL=μ+3σn=95.4+30.505=95.4+0.6696=96.07

Lower control limits for the x¯chart:

LCL=μ−3σn=95.4−30.505=95.4−0.6696=94.73

X-bar chart:

Software procedure:

Step-by-step software procedure to obtain the X-bar chart using EXCEL:

Open an EXCEL file.
Enter the observation.
Enter X-double bar in a new cell B1, in cell B2 enter a formula “=Average(A2:A21)”.
Click Enter.
Click on Insert > select Insert Line chart icon.
Click on the chart > select Layout from the Chart Tools.
Select Chart Title > Above Chart.
Enter X-bar Chart in the dialog box.

Thus, the control limits for the x¯ chart are UCL=96.07 and LCL=94.73.

c.

To determine

Explain whether any of the 20 sample means indicate that the process is out of control or not.

c.

Expert Solution

Explanation of Solution

From the x¯ chart, it is observed that all the sample means lie within UCL and LCL.

Thus, the 20 sample means do not indicate that the process was out of control.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 19, Problem 16SE

a.

To determine

Find the estimate of the mean when the process is in control.

a.

Expert Solution

Answer to Problem 16SE

The estimate of the mean for the production process that is in control is 95.4.

Explanation of Solution

Calculation:

The means for 20 samples of a production process are provided.

The estimate of the mean for the production process is given below:

μ=∑x¯n=(95.72+95.44+95.40+95.50+95.56+95.72+95.60+95.24+95.46+95.44+95.80+95.22+94.82+95.78+95.18+95.32+95.08+95.22+95.04+95.46)20=1,90820=95.4

Thus, the estimate of the mean for the production process that is in control is 95.4.

b.

To determine

Construct a x¯ control chart for the production process.

b.

Expert Solution

Answer to Problem 16SE

Output obtained using MINITAB software is given below:

Modern Business Statistics with Microsoft Excel (MindTap Course List), Chapter 19, Problem 16SE

Explanation of Solution

Calculation:

Upper control limits for the x¯chart:

UCL=μ+3σn=95.4+30.505=95.4+0.6696=96.07

Lower control limits for the x¯chart:

LCL=μ−3σn=95.4−30.505=95.4−0.6696=94.73

X-bar chart:

Software procedure:

Step-by-step software procedure to obtain the X-bar chart using EXCEL:

Open an EXCEL file.
Enter the observation.
Enter X-double bar in a new cell B1, in cell B2 enter a formula “=Average(A2:A21)”.
Click Enter.
Click on Insert > select Insert Line chart icon.
Click on the chart > select Layout from the Chart Tools.
Select Chart Title > Above Chart.
Enter X-bar Chart in the dialog box.

Thus, the control limits for the x¯ chart are UCL=96.07 and LCL=94.73.

c.

To determine

Explain whether any of the 20 sample means indicate that the process is out of control or not.

c.

Expert Solution

Explanation of Solution

From the x¯ chart, it is observed that all the sample means lie within UCL and LCL.

Thus, the 20 sample means do not indicate that the process was out of control.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Chapter 19, Problem 16SE

a.

To determine

Find the estimate of the mean when the process is in control.

a.

Expert Solution

Answer to Problem 16SE

The estimate of the mean for the production process that is in control is 95.4.

Explanation of Solution

Calculation:

The means for 20 samples of a production process are provided.

The estimate of the mean for the production process is given below:

μ=∑x¯n=(95.72+95.44+95.40+95.50+95.56+95.72+95.60+95.24+95.46+95.44+95.80+95.22+94.82+95.78+95.18+95.32+95.08+95.22+95.04+95.46)20=1,90820=95.4

Thus, the estimate of the mean for the production process that is in control is 95.4.

b.

To determine

Construct a x¯ control chart for the production process.

b.

Expert Solution

Answer to Problem 16SE

Output obtained using MINITAB software is given below:

Modern Business Statistics with Microsoft Excel (MindTap Course List), Chapter 19, Problem 16SE

Explanation of Solution

Calculation:

Upper control limits for the x¯chart:

UCL=μ+3σn=95.4+30.505=95.4+0.6696=96.07

Lower control limits for the x¯chart:

LCL=μ−3σn=95.4−30.505=95.4−0.6696=94.73

X-bar chart:

Software procedure:

Step-by-step software procedure to obtain the X-bar chart using EXCEL:

Open an EXCEL file.
Enter the observation.
Enter X-double bar in a new cell B1, in cell B2 enter a formula “=Average(A2:A21)”.
Click Enter.
Click on Insert > select Insert Line chart icon.
Click on the chart > select Layout from the Chart Tools.
Select Chart Title > Above Chart.
Enter X-bar Chart in the dialog box.

Thus, the control limits for the x¯ chart are UCL=96.07 and LCL=94.73.

c.

To determine

Explain whether any of the 20 sample means indicate that the process is out of control or not.

c.

Expert Solution

Explanation of Solution

From the x¯ chart, it is observed that all the sample means lie within UCL and LCL.

Thus, the 20 sample means do not indicate that the process was out of control.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 19, Problem 16SE

a.

To determine

Find the estimate of the mean when the process is in control.

a.

Expert Solution

Answer to Problem 16SE

The estimate of the mean for the production process that is in control is 95.4.

Explanation of Solution

Calculation:

The means for 20 samples of a production process are provided.

The estimate of the mean for the production process is given below:

μ=∑x¯n=(95.72+95.44+95.40+95.50+95.56+95.72+95.60+95.24+95.46+95.44+95.80+95.22+94.82+95.78+95.18+95.32+95.08+95.22+95.04+95.46)20=1,90820=95.4

Thus, the estimate of the mean for the production process that is in control is 95.4.

b.

To determine

Construct a x¯ control chart for the production process.

b.

Expert Solution

Answer to Problem 16SE

Output obtained using MINITAB software is given below:

Modern Business Statistics with Microsoft Excel (MindTap Course List), Chapter 19, Problem 16SE

Explanation of Solution

Calculation:

Upper control limits for the x¯chart:

UCL=μ+3σn=95.4+30.505=95.4+0.6696=96.07

Lower control limits for the x¯chart:

LCL=μ−3σn=95.4−30.505=95.4−0.6696=94.73

X-bar chart:

Software procedure:

Step-by-step software procedure to obtain the X-bar chart using EXCEL:

Open an EXCEL file.
Enter the observation.
Enter X-double bar in a new cell B1, in cell B2 enter a formula “=Average(A2:A21)”.
Click Enter.
Click on Insert > select Insert Line chart icon.
Click on the chart > select Layout from the Chart Tools.
Select Chart Title > Above Chart.
Enter X-bar Chart in the dialog box.

Thus, the control limits for the x¯ chart are UCL=96.07 and LCL=94.73.

c.

To determine

Explain whether any of the 20 sample means indicate that the process is out of control or not.

c.

Expert Solution

Explanation of Solution

From the x¯ chart, it is observed that all the sample means lie within UCL and LCL.

Thus, the 20 sample means do not indicate that the process was out of control.

Answer 6

Chapter 19, Problem 16SE

a.

To determine

Find the estimate of the mean when the process is in control.

a.

Expert Solution

Answer to Problem 16SE

The estimate of the mean for the production process that is in control is 95.4.

Explanation of Solution

Calculation:

The means for 20 samples of a production process are provided.

The estimate of the mean for the production process is given below:

μ=∑x¯n=(95.72+95.44+95.40+95.50+95.56+95.72+95.60+95.24+95.46+95.44+95.80+95.22+94.82+95.78+95.18+95.32+95.08+95.22+95.04+95.46)20=1,90820=95.4

Thus, the estimate of the mean for the production process that is in control is 95.4.

Answer 7

Chapter 19, Problem 16SE

a.

To determine

Find the estimate of the mean when the process is in control.

Answer 8

a.

Expert Solution

Answer to Problem 16SE

The estimate of the mean for the production process that is in control is 95.4.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Calculation:

The means for 20 samples of a production process are provided.

The estimate of the mean for the production process is given below:

μ=∑x¯n=(95.72+95.44+95.40+95.50+95.56+95.72+95.60+95.24+95.46+95.44+95.80+95.22+94.82+95.78+95.18+95.32+95.08+95.22+95.04+95.46)20=1,90820=95.4

Thus, the estimate of the mean for the production process that is in control is 95.4.

Answer 13

b.

To determine

Construct a x¯ control chart for the production process.

b.

Expert Solution

Answer to Problem 16SE

Output obtained using MINITAB software is given below:

Modern Business Statistics with Microsoft Excel (MindTap Course List), Chapter 19, Problem 16SE

Explanation of Solution

Calculation:

Upper control limits for the x¯chart:

UCL=μ+3σn=95.4+30.505=95.4+0.6696=96.07

Lower control limits for the x¯chart:

LCL=μ−3σn=95.4−30.505=95.4−0.6696=94.73

X-bar chart:

Software procedure:

Step-by-step software procedure to obtain the X-bar chart using EXCEL:

Open an EXCEL file.
Enter the observation.
Enter X-double bar in a new cell B1, in cell B2 enter a formula “=Average(A2:A21)”.
Click Enter.
Click on Insert > select Insert Line chart icon.
Click on the chart > select Layout from the Chart Tools.
Select Chart Title > Above Chart.
Enter X-bar Chart in the dialog box.

Thus, the control limits for the x¯ chart are UCL=96.07 and LCL=94.73.

Answer 14

b.

To determine

Construct a x¯ control chart for the production process.

Answer 15

b.

Expert Solution

Answer to Problem 16SE

Output obtained using MINITAB software is given below:

Modern Business Statistics with Microsoft Excel (MindTap Course List), Chapter 19, Problem 16SE

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Calculation:

Upper control limits for the x¯chart:

UCL=μ+3σn=95.4+30.505=95.4+0.6696=96.07

Lower control limits for the x¯chart:

LCL=μ−3σn=95.4−30.505=95.4−0.6696=94.73

X-bar chart:

Software procedure:

Step-by-step software procedure to obtain the X-bar chart using EXCEL:

Open an EXCEL file.
Enter the observation.
Enter X-double bar in a new cell B1, in cell B2 enter a formula “=Average(A2:A21)”.
Click Enter.
Click on Insert > select Insert Line chart icon.
Click on the chart > select Layout from the Chart Tools.
Select Chart Title > Above Chart.
Enter X-bar Chart in the dialog box.

Thus, the control limits for the x¯ chart are UCL=96.07 and LCL=94.73.

Answer 20

c.

To determine

Explain whether any of the 20 sample means indicate that the process is out of control or not.

c.

Expert Solution

Explanation of Solution

From the x¯ chart, it is observed that all the sample means lie within UCL and LCL.

Thus, the 20 sample means do not indicate that the process was out of control.

Answer 21

c.

To determine

Explain whether any of the 20 sample means indicate that the process is out of control or not.

Answer 22

c.

Expert Solution

Explanation of Solution

From the x¯ chart, it is observed that all the sample means lie within UCL and LCL.

Thus, the 20 sample means do not indicate that the process was out of control.

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

Ch. 19.2 - 1. A process that is in control has a mean of =...Ch. 19.2 - 2. Twenty-five samples, each of size 5, were...Ch. 19.2 - Prob. 3E Ch. 19.2 - Prob. 4E Ch. 19.2 - Prob. 5E Ch. 19.2 - Prob. 6E Ch. 19.2 - Prob. 7E Ch. 19.2 - Prob. 8E Ch. 19.2 - Prob. 9E Ch. 19.3 - 10. For an acceptance sampling plan with n = 25...

Find the estimate of the mean when the process is in control.

Concept explainers

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Find the estimate of the mean when the process is in control.

Answer to Problem 16SE

Explanation of Solution

Construct a x¯ control chart for the production process.

Answer to Problem 16SE

Explanation of Solution

Explain whether any of the 20 sample means indicate that the process is out of control or not.

Explanation of Solution

Want to see more full solutions like this?

Chapter 19 Solutions