This exercise shows that the signed-rank test can be used with paired data. Two gauges that measure tire tread depth are being compared. Ten different locations on a tire are measured once by each gauge. The results, in mm, are presented in the following table. Location Gauge 1 Gauge 2 Difference 3.95 3.80 0.15 3.23 3.30 -0.07 3 3.60 3.59 0.01 4 3.48 3.61 -0.13 3.89 3.88 0.01 3.76 3.73 0.03 3.45 3.56 -0.11 8 3.01 3.02 -0.01 3.82 3.77 0.05 10 3.44 3.49 -0.05 Assume the differences are a sample from an approximately symmetric population with mean µ. Use the Wilcoxon signed-rank test to test H, : µ = 0 versus H : µ # 0.

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This exercise shows that the signed-rank test can be used with paired data. Two gauges that
measure tire tread depth are being compared. Ten different locations on a tire are measured
once by each gauge. The results, in mm, are presented in the following table.
Location
Gauge 1
Gauge 2
Difference
3.95
3.80
0.15
3.23
3.30
-0.07
3
3.60
3.59
0.01
4
3.48
3.61
-0.13
3.89
3.88
0.01
3.76
3.73
0.03
3.45
3.56
-0.11
8
3.01
3.02
-0.01
3.82
3.77
0.05
10
3.44
3.49
-0.05
Assume the differences are a sample from an approximately symmetric population with
mean µ. Use the Wilcoxon signed-rank test to test H, : µ = 0 versus H : µ # 0.
Transcribed Image Text:This exercise shows that the signed-rank test can be used with paired data. Two gauges that measure tire tread depth are being compared. Ten different locations on a tire are measured once by each gauge. The results, in mm, are presented in the following table. Location Gauge 1 Gauge 2 Difference 3.95 3.80 0.15 3.23 3.30 -0.07 3 3.60 3.59 0.01 4 3.48 3.61 -0.13 3.89 3.88 0.01 3.76 3.73 0.03 3.45 3.56 -0.11 8 3.01 3.02 -0.01 3.82 3.77 0.05 10 3.44 3.49 -0.05 Assume the differences are a sample from an approximately symmetric population with mean µ. Use the Wilcoxon signed-rank test to test H, : µ = 0 versus H : µ # 0.
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