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.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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