In Problem, hypothesis tests were devised to ascertain whether or not out of three operators, "A," "B," and "C," working in a toll manufacturing facility, operator "A" was deemed to be more safety conscious. The data below, showing the time in months between occurrences of safety violations for each operator, was to be used to test these hypotheses.
|
A
|
1.31
|
0.15
|
3.02
|
3.17
|
4.84
|
0.71
|
0.70
|
1.41
|
2.68
|
0.68
|
|
B
|
1.94
|
3.21
|
2.91
|
1.66
|
1.51
|
0.30
|
0.05
|
1.62
|
6.75
|
1.29
|
|
C
|
0.79
|
1.22
|
0.65
|
3.90
|
0.18
|
0.57
|
7.26
|
0.43
|
0.96
|
3.76
|
Unfortunately, the random variable in question is exponentially distributed; the sample size of 10 is considerably smaller than is required for a normal approximation to be valid for the sampling distribution of the sample mean; and therefore no standard hypothesis test could be used.
Convert the data to a form that will be appropriate for carrying out a one-sample Wilcoxon signed rank test to compare operator "A" to operator "B," and a second one-sample Wilcoxon signed rank test to compare operator "A" to operator "C." Interpret your results. Can operator "A" truly be said to be more more safety conscious than either "B" or "C"? If yes, at what signi?cance level?