{Exercise 13.07} Three different methods for assembling a product were proposed

Question

{Exercise 13.07}

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 = 10,750; SSTR = 4,550.

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

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).

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

Explanation / Answer

The critical value of F for(2,27 ) is 3.3541 Since F calculated is less than F tabulated, we fail to reject 0 and conclude that there is no difference in the means for the three assemble methods. Source of variation SS DF MSS F Treatments 4550 2 4550/2 =2275 2275/229.9296=1.20 Error 10750-4550=6200 27 6200/27=229.6296 Total 10750 29

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