Measurements on the bending and twisting stiffness of 12 randomly selected tennisracquets are given in the following table.Racquet (X) Bending (Y) TwistingNumberStiffnessStiffness141922724072313363200436021152571826622304424384359194346158556225474305441235789101112(X₂) RankBending Stiffness765412211109(Y₂) RankTwisting Stiffness78452101231119Note 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 theranks 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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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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Stalk Length (cm) Root Length (cm) Leaf Count Plant 1 10.1 4.4 35 Plant 2 21.55 8.2 27 Plant 3 21.7 5.5 40 Plant 4 18.6 4.2 42 Plant 5 19.5 6 38 Plant 6 18.5 5 36 Plant 7 17 5 39 Plant 8 18.6 5.1 45 Plant 9 17.8 5.2 26 Plant 10 17.3 5.2 37 Plant 11 17.6 6.2 41 Plant 12 11.7 2.8 40 Plant 13 21 5 42 Plant 14 18.1 6.1 23 Plant 15 21 6.2 33 Plant 16 17.2 2.8 46 Plant 17 15.45 2.7 40 Plant 18 17.1 2.5 34 Plant 19 21 4.9 36 Plant 20 13.65 2.5 35 Plant 21 16.5 6.35 21 Plant 22 20.2 3.8 35 Plant 23 18.6 5.3 41 Plant 24 22 6.4 36 Plant 25 19.7 5.5 9 Plant 26 17.8 3.7 43 Plant 27 21 6.2 36 Plant 28 17.8 5.6 45 Plant 29 18.2 6 24 Plant 30 18.5 4.7 38 Identify the random variable used in the given data set and find the following: A. Central Tendency (Mean, Median, Mode - whichever is appropriate to the variable). B. Dispersion (Range, Variance, Standard Deviation, Coefficient of Variation - whichever is appropriate to the…
Wild irises are beautiful flowers found throughout the United States, Canada, and northern Europe. This problem concerns the length of the sepal (leaf-like part covering the flower) of different species of wild iris. Data are based on information taken from an article by R. A. Fisher in Annals of Eugenics (Vol. 7, part 2, pp. 179 -188). Measurements of sepal length in centimeters from random samples of Iris setosa (I), Iris versicolor (II), and Iris virginica (III) are as follows below. I II III 5.9 5.8 6.9 4.8 6.5 5.6 4.6 6.4 4.9 5.7 4.3 7.7 4.8 5.8 5.6 5.4 6.3 6.3 5.8 5.5 6.6 Shall we reject or not reject the claim that there are no differences among the population means of sepal length for the different species of iris? Use a 5% level of significance. (b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.) SSTOT = SSBET = SSW = Find d.f.BET, d.f.W, MSBET, and MSW. (Use 4 decimal places for MSBET, and…

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