In an experiment to compare two different materials A and

Chapter 10, Problem 16

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In an experiment to compare two different materials A and B that might be used for manufacturing the heels of mens 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 10.46. 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 of Exercise 1, (b) the Wilcoxon signedranks test of Exercise 15, and (c) the paired t test. Table 10.46 Data for Exercise 16 Pair Material A Material B 1 6.6 7.4 2 7.0 5.4 3 8.3 8.8 4 8.2 8.0 5 5.2 6.8 6 9.3 9.1 7 7.9 6.3 8 8.5 7.5 9 7.8 7.0 10 7.5 6.6 11 6.1 4.4 12 8.9 7.7 13 6.1 4.2 14 9.4 9.4 15 9.1