An experiment was conducted to compare the strengths of two types of papers: one a standard paper of a specified weight and the other the same standard paper treated with a chemical substance. Ten pieces of each type of paper, randomly selected from production, produced the strength measurements shown in Table 15.5. Test the null hypothesis of no difference in the distributions of strengths for the two types of paper versus the alternative hypothesis that the treated paper tends to be stronger (that is, its distribution of strength measurements is shifted to the right of the corresponding distribution for the untreated paper).

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Table 15.5 Strength Measurements (and Their Ranks) for Two Types of Paper Standard 1 Treated 2 Rank sum 1.21 (2) 1.49 (15) 1.43 (12) 1.37 (7.5) 1.35 (6) 1.67 (20) 1.51 (17) 1.50 (16) 1.39 (9) 1.17 (1) 1.31 (5) 1.29 (3.5) 1.48 (14) 1.52 (18) 1.42 (11) 1.37 (7.5) 1.29 (3.5) 1.44 (13) 1.40 (10) 1.53 (19) T =85.5 T =n,(n,+n,+1T=21085.5=124.5