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.

Assume the differences are a sample from an approximately symmetric population with mean μ. Use the Wilcoxon signed-rank test to test H0 :μ = 0 versus H1 :μ ( 0?

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Location Gauge 1 Gauge 2 Difference 3.95 3.23 3.60 3.48 3.89 3.76 3.45 3.01 3.82 3.44 3.80 3.30 3.59 3.61 3.88 3.73 3.56 3.02 3.77 3.49 0.15 -0.07 0.01 -0.13 0.01 0.03 4 -0.01 0.05 -0.05 10