Measurements on the bending and twisting stiffness of 12 randomly selected tennis racquets are given in the following table. Racquet (X) Bending (Y) Twisting Number Stiffness Stiffness 1 419 227 2 407 231 3 363 200 4 360 211 5 257 182 6 622 304 7 424 384 8 359 194 9 346 158 10 556 225 11 474 305 12 441 235 (X₂) Rank Bending Stiffness 7 6 5 12 8 11 10 9 (Y₂) Rank Twisting Stiffness 7 8 5 2 10 12 3 6 E 11 9 Note for the original observations Σ Χ = 5028, ΣΥ = 2856, ΣΧΥ = 1233987, Σ(X- X)² = 105446, (Y-Y)²=44154 and for the ranks of the observations X, = ΣΥ = 78, Σ.Χ.Υ. = 623, and Σ(X - Χ,) = Σ(Υ - Υ,)" = 143, (a) Find the value of the Spearman's rank correlation coefficient, rg between the ranks of bending and twisting stiffness. (b) Stating appropriate hypotheses, test for a significant positive correlation be- tween the ranks of the bending and twisting stiffness.
Measurements on the bending and twisting stiffness of 12 randomly selected tennis racquets are given in the following table. Racquet (X) Bending (Y) Twisting Number Stiffness Stiffness 1 419 227 2 407 231 3 363 200 4 360 211 5 257 182 6 622 304 7 424 384 8 359 194 9 346 158 10 556 225 11 474 305 12 441 235 (X₂) Rank Bending Stiffness 7 6 5 12 8 11 10 9 (Y₂) Rank Twisting Stiffness 7 8 5 2 10 12 3 6 E 11 9 Note for the original observations Σ Χ = 5028, ΣΥ = 2856, ΣΧΥ = 1233987, Σ(X- X)² = 105446, (Y-Y)²=44154 and for the ranks of the observations X, = ΣΥ = 78, Σ.Χ.Υ. = 623, and Σ(X - Χ,) = Σ(Υ - Υ,)" = 143, (a) Find the value of the Spearman's rank correlation coefficient, rg between the ranks of bending and twisting stiffness. (b) Stating appropriate hypotheses, test for a significant positive correlation be- tween the ranks of the bending and twisting stiffness.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
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