Spearman's Rank Correlation Coefficientnn56789101112-1α/2Critical Values of Spearman's RankCorrelation Coefficient rα = 0.10α = 0.05.900.829.714.643.600564.536.503.886.786x/2.738.700.648.618.587α = 0.02.943.893.833.783745.709.678α = 0.01.929.881.833.794.755.727- X The table below lists the numbers of audience impressions (in hundreds of millions) listening to songs and the corresponding numbers of albums sold (in hundreds of thousands). Does itappear that album sales are affected very strongly by the number of audience impressions? Use a significance level of α = 0.05.24825151412Click the icon to view the critical values of Spearman's rank correlation coefficient.Audience Impressions 23Albums Sold13∞Determine the null and alternative hypotheses for this test. Choose the correct answer below.O A. Ho:r₂ = 0H₁: rs #0O C. Ho: Ps #0H₁: Ps=01511OB.Ho: rs #0H₁: rs = 0OD. Ho: Ps = 0H₁: Ps #0226181026141815D

Given data: Audience Impressions 23 24 25 14 15 22 18 26 18 Albums Sold 13 8 15 12 11 6 10 14 15 With the standard denotation of the rank correlation coefficient, at the population level, ρ it is set up: H0:ρs=0, i.e., album sales are not affected by audience impressions. H1:ρs≠0, i.e., album sales are affected by audience impressions. So option (D) is correct. The observed values are represented in terms of ranks as follows: Audience impressions (x) Albums sold (y) Rank of x; Rx Rank of y; Ry d=Rx-Ry d2 23 13 4 4 0 0 24 8 3 8 -5 25 25 15 2 1.5 0.5 0.25 14 12 9 5 4 16 15 11 8 6 2 4 22 6 5 9 -4 16 18 10 6.5 7 -0.5 0.25 26 14 1 3 -2 4 18 15 6.5 1.5 5 25 As for the defined variable x, the observation 18 is repeated 2 times for the corresponding ranks of 6 and 7, and the average of the corresponding ranks, i.e., 6+72=6.5 is assigned for observation 18. So the no. of repeated rank m1=2 As for the defined variable y, observation 15 is repeated 2 times for the corresponding ranks of 1 and 2, and the average of the corresponding ranks, i.e., 1+22=1.5 is assigned for observation 18. So the no. of repeated rank m2=2. For the no. of repeated ranks (denoted as m), the Spearman rank correlation coefficient is obtained as: ρ=1-6∑d2+∑mm2-112nn2-1=1-6×90.5+2×22-112+2×22-1129×92-1≈0.2375 For the two-tailed test with no. of observations, n=9 the critical value is interpreted from the given table for α=0.05 as: n ... α=0.05 ... 9 ... 0.700 For this two-tiled test, the decision rule is: accept H0 is -rs <ρ<rs. Since -rs =-0.700<ρ =0.2375<rs =0.700, H0 is failed to be rejected. The album sales are interpreted to be not affected by audience impressions.