Two materials X and Y were tested for wear using a standard laboratory procedure. The results of the experiment, based on 12 specimens were as follows (the results are coded for convenience): Material X Material Y 1 Sample size nx=12 ny-12 2 Specimen 1 41.017 47.414 3 Specimen 2 38.874 40.98 4 Specimen 3 42.903 40.261 5 Specimen 4 39.406 41.91 6 Specimen 5 39.254 41.362 7 Specimen 6 41.187 41.928 8. Specimen 7 39.148 42.288 9 Specimen 8 40.303 42.02 10 Specimen 9 38.845 41.672 11 Specimen 10 40.061 38.998 12 Specimen 11 39.077 42.98 13 Specimen 12 42.221 42.041 14 Sample Mean 40.191 41.988 15 Sample Standard Deviation 1.3668 1.9991 a) Test the hypothesis that the variance of the probability distribution of the wear of material X is not significantly different from that of material Y. State any assumptions you need to make. Let a = 0.05 (40 marks). b) It is known that the two standard deviations are equal o = 02. Test the hypothesis that the mean wear of material Y is not significantly higher than that of material X. Let a = 0.05 (30 marks). c) Consider that the results were collected in pairs. Use the paired t-test to investigate if the mean wear of material Y is significantly higher than that of material X. Let a = 0.05 State your assumptions (30 marks).