Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 30 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by10 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. The following results were obtained: ; . SST:10,700 SSTR:4500 a. Set up the ANOVA table for this problem (to 2 decimals, if necessary). Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value (to 4 decimals) Treatments Error Total b.Use to test for any significant difference in the means for the three assembly methods. Calculate the value of the test statistic (to 2 decimals). The P-value is_______

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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Three different methods for assembling a product were proposed by an industrial engineer. To investigate the

number of units assembled correctly with each method, 30 employees were randomly selected and randomly

assigned to the three proposed methods in such a way that each method was used by10 workers. The number of

units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting

data set. The following results were obtained: ; . SST:10,700 SSTR:4500

a. Set up the ANOVA table for this problem (to 2 decimals, if necessary).

Source of Variation

Sum of Squares

Degrees of Freedom

Mean Square

p-value (to 4 decimals)

Treatments

Error

Total

b.Use to test for any significant difference in the means for the three assembly methods.

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

The P-value is_______

What is your conclusion? _________________________

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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