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2. A company wishes to purchase one of five different machines A,B,C,D, and
E. In an experiment to decide whether there is a difference in performance of
the machines five experienced operators each work on the machines. The table
below shows the number of units produced. Test the hypothesis that there is no
difference among the machines at the (a)0.05 level of significance, (b) 0.01
level of significance.
machine units produced
A 68 72 75 42 53
B 72 52 63 55 48
C 60 82 65 77 75
D 48 61 57 64 50
E 64 65 70 68 53
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The following provides a hypothesis test to determine if there is a significant difference in the performance of five different machines. An F-test is performed to test the null that the output from each machine is equal. H0: D1=D2=D3=D4=D5
The question here is to compare the population means of the five groups using ANOVA.
The null hypothesis will be that all population means are equal, the alternative hypothesis is that at least one mean is different:
H0: D1=D2=D3=D4=D5 vs.
H1: at least one D is different
The grand mean of a set of samples is the total of all the data values divided by the total sample size. Dgm=62.36
The total variation (not variance) is comprised the sum of the squares of the differences of each mean with the grand mean. There is the between group variation and the within group variation. The whole idea behind the analysis of variance is to compare the ratio of between group variance to within group variance. If the variance caused by the interaction between the samples is much larger when compared to the variance that appears within each group, ...
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