Question

The deflection temperature under load for two different types of plastic pipe is being investigated. Two random samples of 15 pipe specimens are tested, and the deflection temperatures observed are as follows (in °F): Type 1: 151 133 150 132 139 138 152 130 134 158 137 155 139 123 150 Type 2: 122 142 151 146 125 121 130 145 142 137 143 133 134 148 137 (a) Use the Wilcoxon rank-sum test for the pipe deflection temperature experimentto test if one pipe type has a higher mean deflection temperature than the other. If a = 0.05, what are your conclusions? W1 = W2= i Should you reject or fail to reject Ho? Ho. (b) Use the normal approximation for the Wilcoxon rank-sum test. Assume that a =0.05. Find the approximate P-value for this test. Round your answer to 4 decimal places. P-value = i

Answer 1

Sample Value Rank Rank (Adjusted for ties) 2 121 1 2 122 2 2 1 123 3 3 2 125 4 4 1 130 5 5.5 2 130 6 5.5 1 132 7 7 1 133 8 8.5 2 133 9 8.5 1 134 10 10.5 2 134 11 10.5 1 137 12 13 2 137 13 13 2 137 14 13 1 138 15 15 1 139 16 16.5 1 139 17 16.5 2 142 18 18.5 2 142 19 18.5 2 143 20 20 2 145 21 21 2 146 22 22 2 148 23 23 1 150 24 24.5 1 150 25 24.5 1 151 26 26.5 2 151 27 26.5 1 152 28 28 1 155 29 29 1 158 30 30

Provided information d=0.05 a) W;= 3+5.5+ 7 + 8.5 +10.5 +13 + 15 + 16.5+ 16.5+ 24.5+ 24.5+ 26.5+ 28 +29+ 30 W, = 258 W2 = 1+ 2+ 4 + 5.5 +8.5 +10.5+ 13+13 +18.5+ 18.5+20+2) + 22 +23 + 26.5 W2 = 207 The null and alternative hypo Ho: Median (difference = 0 H: Median difference to Test statistic (R) = Wi-258 z-statistic=R-niin,+ n2+) 2 Vinz (n,+na+1)/12

Z = 258-15(15+15+1) 2 1515 (15+15+12/12 Z = 1.058 Z = 1.64 Q : Should you reject or fail to reject Ho? Do not rejects Ho b) P-value = P(Z > 1.058) P-value = 0.1451

Thank You !