Three different methods for assembling a product were proposed by an industrial

Question

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 = 10,760; SSTR = 4,530.

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).

Explanation / Answer

here for above test:

SSE =SST-SSTR =10760-4530=6230

degree of freedom for Treatments df(TR) =groups-1=k-1=3-1=2

and degree of freedom for error df(error) =N-k=30-3=27

hence MS(treatments) =SSTr/df(TR) =4530/2=2265

and MSE =SSE/df(error) =6230/27=230.74

hence test statistic F =MS(treatments)/MSE =9.82

for 0.05 level and (2,27) degree of freedom critical value F =3.354

as test statistic is highe than critical value we reject null hypothesis and conclude that at least two group have different means

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