11a. You may need to use the appropriate appendix table or technology to answer this question. Product filling weights are normally distributed with a mean of 450 grams and a standard deviation of 30 grams. (a) - Develop the control limits for the x chart for a sample of size 10. (Round your answers to two decimal places.) UCL=? LCL=? - Develop the control limits for the x chart for a sample of size 20. (Round your answers to two decimal places.) UCL=? LCL=? - Develop the control limits for the x chart for a sample of size 30. (Round your answers to two decimal places.) UCL=? LCL=? (b) What happens to the control limits as the sample size is increased? - The LCL comes closer to the process mean and the UCL moves farther from the process mean as the sample size is increased. - Both control limits move farther from the process mean as the sample size is increased. - Both control limits come closer to the process mean as the sample size is increased.The sample size does not affect the control limits. - The UCL comes closer to the process mean and the LCL moves farther from the process mean as the sample size is increased. (c) What happens when a Type I error is made? - The process will be declared in control and allowed to continue when the process is actually out of control. - The process will be declared out of control and adjusted when the process is actually in control.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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11a. You may need to use the appropriate appendix table or technology to answer this question.

Product filling weights are normally distributed with a mean of 450 grams and a standard deviation of 30 grams.

(a)

- Develop the control limits for the x chart for a sample of size 10. (Round your answers to two decimal places.)

UCL=? LCL=?

- Develop the control limits for the x chart for a sample of size 20. (Round your answers to two decimal places.)

UCL=? LCL=?

- Develop the control limits for the x chart for a sample of size 30. (Round your answers to two decimal places.)

UCL=? LCL=?

(b)

What happens to the control limits as the sample size is increased?

- The LCL comes closer to the process mean and the UCL moves farther from the process mean as the sample size is increased.

- Both control limits move farther from the process mean as the sample size is increased.

- Both control limits come closer to the process mean as the sample size is increased.The sample size does not affect the control limits.

- The UCL comes closer to the process mean and the LCL moves farther from the process mean as the sample size is increased.

(c)

What happens when a Type I error is made?

- The process will be declared in control and allowed to continue when the process is actually out of control.

- The process will be declared out of control and adjusted when the process is actually in control.

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 + ...

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