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(a) The abrasion loss of each brake pad was measures (mg) in a set of bicycle br

ID: 3234667 • Letter: #

Question


(a) The abrasion loss of each brake pad was measures (mg) in a set of bicycle brakes. The result of 14 trials are shown below. Apply a Wilcoxon signed-rank test to the data to test the null hypothesis that the mean difference in abrasion loss between left and right pads is zero. Use the 1% level of significance. Comment on any assumptions which you need to make. (b) If the data above followed a normal distribution, what test would you use to test the mean difference in abrasion loss between left and right pads

Explanation / Answer

The observed left pad abrasion loss is 208,196,142,190,185,179,198,202,196,135,187,172,179,191

The observed right pad abrasion loss is 205,191,137,210,183,204,191,201,195,121,201,192,201,192

The observed difference between left and right pad is 3 5 5 -20 2 -25 7 1 1 14 -14 -20 -22 -1

Ordered Absolute Values of Differences between left and right pad is -1, 1, 1, 2, 3, 5, 5, 7, -14, 14, -20, -20, -22, -25

The signed ranks of the observed diffrences are -1, 1, 1, 4, 5, 6, 6, 8, -9, 9, -11, -11, -13, -14

The signed ranks (tied ranks) of the observed diffrences are -2, 2 , 2, 4, 5, 6.5, 6.5, 8, -9.5, 9.5, -11.5, -11.5, -13, -14

Hypothesis are -

H0: The median difference between abrasion loss of left and right pads is zero versus

H1: The median difference between abrasion loss of left and right pads is not zero,

=0.01

Sum of positive ranks W+ = 43.5

Sum of negative ranks W- = 61.5

The minimum of positive and negative ranks is 43.5

For n=14, and =0.01, critical value of W is 12.

We do not reject H0 because 43.5 > 12. Therefore, we do not have statistically significant evidence at =0.01, to show that the median difference in abrasion loss of left and right pads is not zero (i.e., that there is a significant difference in abrasion loss of left and right pads).

(b) If the above data follows a normal distribution, and n < 30, we can do matched-pairs t-test.