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TABLE 15.5 An experiment was conducted to compare the strengths of two types of kraft papers: one a standard kraft paper of a specified weight and the other the same standard kraft 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 *Since the value of T = 34 lies to the right of the mean 22, the subtraction of .5 in using the normal approxi- mation takes into account the lower limit of the bar above the value 34 in the probability distribution of T. types of paper versus the alternative hypothesis that the treated paper tends to be stronger (i.e., its distribution of strength measurements is shifted to the right of the corresponding distribution for the untreated paper). Strength Measurements (and Their Ranks) for Two Types of Paper Standard 1 Treated 2 1.21 (2) 1.43 (12) 1.35 (6) 1.51 (17) 1.39 (9) 1.17 (1) 1.48 (14) 1.42 (11) 1.29 (3.5) 1.40 (10) Rank sum 1.49 (15) 1.37 (7.5) 1.67 (20) 1.50 (16) 1.31 (5) 1.29 (3.5) 1.52 (18) 1.37 (7.5) 1.44 (13) 1.53 (19) T₁ = 85.5 T₁ = m₁(m₁ + 1₂ + 1) - T₁ = 210 - 85.5=124.5

TABLE 15.5 An experiment was conducted to compare the strengths of two types of kraft papers: one a standard kraft paper of a specified weight and the other the same standard kraft 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 *Since the value of T = 34 lies to the right of the mean 22, the subtraction of .5 in using the normal approxi- mation takes into account the lower limit of the bar above the value 34 in the probability distribution of T. types of paper versus the alternative hypothesis that the treated paper tends to be stronger (i.e., its distribution of strength measurements is shifted to the right of the corresponding distribution for the untreated paper). Strength Measurements (and Their Ranks) for Two Types of Paper Standard 1 Treated 2 1.21 (2) 1.43 (12) 1.35 (6) 1.51 (17) 1.39 (9) 1.17 (1) 1.48 (14) 1.42 (11) 1.29 (3.5) 1.40 (10) Rank sum 1.49 (15) 1.37 (7.5) 1.67 (20) 1.50 (16) 1.31 (5) 1.29 (3.5) 1.52 (18) 1.37 (7.5) 1.44 (13) 1.53 (19) T₁ = 85.5 T₁ = m₁(m₁ + 1₂ + 1) - T₁ = 210 - 85.5=124.5

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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TABLE 15.5 An experiment was conducted to compare the strengths of two types of kraft papers: one a standard kraft paper of a specified weight and the other the same standard kraft 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 *Since the value of T = 34 lies to the right of the mean 22, the subtraction of .5 in using the normal approxi- mation takes into account the lower limit of the bar above the value 34 in the probability distribution of T. types of paper versus the alternative hypothesis that the treated paper tends to be stronger (i.e., its distribution of strength measurements is shifted to the right of the corresponding distribution for the untreated paper). Strength Measurements (and Their Ranks) for Two Types of Paper Standard 1 Treated 2 1.21 (2) 1.43 (12) 1.35 (6) 1.51 (17) 1.39 (9) 1.17 (1) 1.48 (14) 1.42 (11) 1.29 (3.5) 1.40 (10) Rank sum 1.49 (15) 1.37 (7.5) 1.67 (20) 1.50 (16) 1.31 (5) 1.29 (3.5) 1.52 (18) 1.37 (7.5) 1.44 (13) 1.53 (19) T₁ = 85.5 T₁ = m₁(m₁ + 1₂ + 1) T₁ = 210 - 85.5=124.5
Transcribed Image Text:TABLE 15.5 An experiment was conducted to compare the strengths of two types of kraft papers: one a standard kraft paper of a specified weight and the other the same standard kraft 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 *Since the value of T = 34 lies to the right of the mean 22, the subtraction of .5 in using the normal approxi- mation takes into account the lower limit of the bar above the value 34 in the probability distribution of T. types of paper versus the alternative hypothesis that the treated paper tends to be stronger (i.e., its distribution of strength measurements is shifted to the right of the corresponding distribution for the untreated paper). Strength Measurements (and Their Ranks) for Two Types of Paper Standard 1 Treated 2 1.21 (2) 1.43 (12) 1.35 (6) 1.51 (17) 1.39 (9) 1.17 (1) 1.48 (14) 1.42 (11) 1.29 (3.5) 1.40 (10) Rank sum 1.49 (15) 1.37 (7.5) 1.67 (20) 1.50 (16) 1.31 (5) 1.29 (3.5) 1.52 (18) 1.37 (7.5) 1.44 (13) 1.53 (19) T₁ = 85.5 T₁ = m₁(m₁ + 1₂ + 1) T₁ = 210 - 85.5=124.5
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