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.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 32PPS
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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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