In an experiment to compare two different materials A and B that might be used for manufacturing the heels of men dress shoes, 15 men were selected and fitted with a new pair of shoes on which one heel was made of material A and one heel was made of material B. At the beginning of the experiment, each heel was 10 millimeters thick. After the shoes had been worn for one
month, the remaining thickness of each heel was measured. The results are given in Table 9.36. Test the null hypothesis that material A is not more durable than material B against the alternative that material A is more durable than material B, by using
(a) the sign test and
(b) the Wilcoxon signed-ranks test.