Answered: productionn line operattes with a mean…

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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Question

A productionn line operattes with a mean fillling weight of 16 oz per conntainer. Over-filling or under-filling presents a serious problem and reqquires the operator to shut down the production line to readjust the filling mechanism. A quality control inspector selects a sample of 30 itemms every hour and makes the deccision of whether to shutt down the line for readjjustment at that time. Supppose that the most recent sample returns a mean of 15.82 oz and a sample standard deviation of 0.8 oz. Assume the significance level (α) is 5%.

A. Using the critical value approach, what is the critical value?

±2.045

±2.042

1.697

1.699

B. What is your conclusion (reject or fail to reject the null)?

Fail to reject the null

Reject the null

C. Using the p-value approach, what is the p-value?

p-value is more than 0.40

p-value is between 0.20 and 0.40

p-value is between 0.05 and 0.10

p-value is between 0.10 and 0.20

p-value is less than 0.05

D. What’s your conclusion (reject or fail to reject the null)? Does the quallity control insppector need to shutt down the productionn line this time?

Reject the null. The quality control inspector needs to shut down the production line this time.

Fail to reject the null. The quality control inspector does not need to shut down the production line this time.

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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