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.

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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
424
384
359
194
346
158
556
225
474
305
441
235
7
8
9
10
11
12
(X₂) Rank
Bending Stiffness
7
6
5
4
12
2
11
10
9
(Y₂) Rank
Twisting Stiffness
7
8
4
5
2
10
12
3
1
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(Χ. – Χ,) = Σ(Υ. - Υ,)2 = 143.
(a) Find the value of the Spearman's rank correlation coefficient, rs 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.
Transcribed Image Text: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 6 622 304 424 384 359 194 346 158 556 225 474 305 441 235 7 8 9 10 11 12 (X₂) Rank Bending Stiffness 7 6 5 4 12 2 11 10 9 (Y₂) Rank Twisting Stiffness 7 8 4 5 2 10 12 3 1 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(Χ. – Χ,) = Σ(Υ. - Υ,)2 = 143. (a) Find the value of the Spearman's rank correlation coefficient, rs 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.
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