{Exercise 13.07 (Algorithmic)} Three different methods for assembling a product

Question

{Exercise 13.07 (Algorithmic)}

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 by 10 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 = 10,780; SSTR = 4,580.

Source of Variation Sum of Squares Degrees of Freedom Mean Square F Treatments Error Total

Explanation / Answer

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

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Use = .05 to test for any significant difference in the means for the three assembly methods.

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

F= MSR/MSE

=2290/229.6296296

=9.97

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The p-value is P(F with df1=2, df2= 27 >9.97) =0.0006 (from F table)

So the p-value is less than 0.01

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Conclusion:

Conclude not all means of the three assembly methods are equal

Sum of Squares Degrees of Freedom Mean Square F Treatments 4580 2 2290 9.972581 Error 6200 27 229.6296296 Total 10780 29

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