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: 243 225 242 224 231 230 244 222 226 250 229 247 231 215 242 Type 2: 214 234 243 238 217 213 222 237 234 229 235 225 226 240 229 (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-i 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

sha) Null is same hypothesis Ho. The deflection temperature for two types of plastic pipes Against Ha : The deflection lemperature for livo lypes of plastic pipes is not same Text stalistic The Test stalistica w is W, = minat nichiti-RI 2 nz (02t1) - R2 W2= 2 the 2 The sizes nint where R R and R2 are the sums of ranks in type I and lype 2 resply decision rule. The critical value based on sample a two-sided level (n,=12=15) and L=0005 is 64. Reject of significance Ho if w€64 compute test statistic The first step is to assign ranks og through 30 to the smallest through largest values in the total sample. The a temperatures listed first in the ordered values smallest assigned nank of are

Ranks Type 1 Type 1 Type I Somple Type 2 412 Type ) Type 2 219 493 2 | 4 239 3 215 2.25 5, 5 29 3 5- 5 292 2. 2.2 22+ 2.25 211 22 2 22 5 8-5 238 229 85 10. S [0.5 2 2 0 211 226 2.3) 2 13 229 13 13 2.29 2 29 230 222 15 249 230 231 16:9 222 2 3 ) 239 L6-5 2.24 2 3 | 18.5 229 23 4 20 8.5 23 5 2.29 2.39 26 22.5 235 217 23 | 2.24 231 22 24b 238 2 | 23 292 229 2 +0 2 + 2 245 245 26.5 28 2. + 2 2 93 219 2-3 26S 29 24 1 30 250 R, - 201 R, : - 25 8 Here R_1 - 2.58 22 2201

AS a ow, ranks check assignment of the sum of the ranks (R 482) will always be equal to 30 (3011) nlnli) = 465 2 Ri+R2 = 258+ 207 2415 and Compute wi n, (nit) 150154 Wia nint 15 (15+1)_258 345-258 = 87 15 (15) +15 (1571)_267 nz (A2+1 _R2 2 W2= nina + 2 138 87 statistic u is we = 345 -207 Thus Test Conclusion: do not reject to because 87764 evidence to have Sefficient do not conclude that the deflection temperature zor two lypes of plastic pipes is diffee we