Answered: At the ? = 0.01 level of significance,…

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 manufacturing company has been selected to assemble a small but important component that will be used during the construction of numerous infrastructure projects. The company anticipates the need to assemble several million components over the next several years. Company engineers select three potential assembly methods: Method A, Method B, and Method C. Management would like to select the method that produces the fewest number parts per 10,000 parts produced that do not meet specifications. It may also be possible that there is no statistical difference between the three methods in which case the lowest cost method will be selected for production. While all parts are checked before leaving the factory, the best method will reduce the number of parts that need to be recycled back into the production process.

To test each method, six batches of 10,000 components are produced using each of the three methods. The number of components out of specification are recorded in the Microsoft Excel Online file below. Analyze the data to determine if there is any difference in the mean number of components that are out of specificaion among the three methods. After conducting the analysis report the findings to the management team.

Compute the sum of squares between treatments (assembly methods).

fill in the blank 2 = 1468
Compute the mean square between treatments (to 1 decimal if necessary).

= 734
Compute the sum of squares due to error.

= 2172
Compute the mean square due to error (to 1 decimal if necessary).

= 14444.8

Set up the ANOVA table for this problem. Round all sum of squares to the nearest whole number. Round all Mean Squares to one decimal place. Round F to two decimal places.

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F
Treatments (Methods)	1468	2	734	5.069060773
Error	2172	15	144.8
Total	3640	17

At the ? = 0.01 level of significance, test whether the means for the three methods are equal.

Calculate the value of the test statistic (to 2 decimals).

=

The p-value is (to 4 decimals): = 0.0208

What is your conclusion for management?
Conclude that all the method means are equal.

I got all the answers correct except for the first part of (6) calculate the value of the test statistic ( to 2 decimals)

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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