15.0p b Table 1.3: Rank sums of minutes per scoring point of Ronaldo and Messi Ranks Player N Mean Rank Sum of Ranks MPP Messi 12 11.08 133.00 Ronaldo 12 13.92 167.00 Total 24 Test Statistics" MPP Mann-Whitney U 89.000 Wilcoxon W 167.000 Z 981 Asymp. Sig. (2-tailed) .326 Exact Sig. [2*(1-tailed Sig.)] .347b a. Grouping Variable: Player b. Not corrected for ties. Table 1.3 contains the rank sums of the ratio of minutes per scoring point for Ronaldo and Messi. Perform the Wilcoxon rank sum test to investigate whether the ratio of minutes per scoring point is significantly higher for Ronaldo than for Messi, using significance level a = 0.10. (i) (2pts) State Ho and Ha. (ii) (2pts) Retrieve the value of the Wilcoxon test statistic from Table 1.3. (ii) (3pts) Compute the mean and the standard deviation of the distribution of the Wilcoxon test statistic. (iv) (3pts) Determine the P-value using the normal approximation. v) (2pts) Draw a clear conclusion, also in common speech. vi) (3pts) Do you expect the results of this test to be identical if the number of scoring points is used stead of the ratio of minutes by scoring point? Why or why not