The plant manager wants to investigate the productivity of three groups of worke

Question

The plant manager wants to investigate the productivity of three groups of workers: those with little, average, and considerable work experience. Since the productivity depends to some degree on the day-to-day variability of the available raw materials, which affects all groups in a similar fashion, the manager suspects that the comparison should be blocked with respect to day. The results (productivity, in percent) from five production days are given in the following table:

                                                    Day

Experience                           1 2   3   4   5

A                                         53 58 49 52 60

B                                          55 57 53 57 64

C                                         60 62 55 64 69

(a). Are there differences in the mean productivity among the three groups?

(b). Has the blocking made a difference?

Explanation / Answer

a)

since p-value = 0.06499 > 0.05

we fail to rejec the null and conclude that there are no significant differences in the mean productivity among the three groups

b)

when we two-way anova

then p-value of groups (Experience) is 0.000396 < 0.05

hence now it has become significant

so , the blocking has made a difference

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Anova: Single Factor SUMMARY Groups Count Sum Average Variance A 5 272 54.4 20.3 B 5 286 57.2 17.2 C 5 310 62 26.5 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 147.733333 2 73.86667 3.4625 0.0649938 3.885294 Within Groups 256 12 21.33333 Total 403.733333 14

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