1. A. study chemically analysed crude-oil samples from three zones of sandstone: Wilhelm, Sub-Muhiuina, Upper. The values of the trace elements XI = vanadium1 X2 = iron, X3 = beryllium, and two measures of hydrocarbons X4 = saturated hydrocarbons and X5 = aromatic hydrocarbons are presented for 56 samples in the data set oil.dat. You will test Ha : p1 = 1.1.; = 11.3 at the o: = .[}5 level. (a) Use R. to calculate the matrices B, W, and A. Use R to calculate the eigenvalues of A, and report the Wilkls lambda {A}. {b} When Hg is true and E n; = n is large, (n1)Inga has approximately a chi-square distribution with g 1} d.f., where p is the dimension of the data vector, and g is the number of groups. Use this information to generate your teat-statistic and obtain a p-value and make a conclusion about HI}. [c] Now, use the MANOVA tool in R to perform the test using ill-Villas1 lambda and compare your results. {The approximation in part Eb) is one of several approximate distributions for Wilks' lambda, so R might be using a different one to perform its teat.) Presumably, you rejected the null hypothesis. The next two questions ask you to perform a follow up analysis. Use flmctions in R. {d} Which of the ve variables show a difference? [ejl Now, test which of the three groups (zones) are different. Run all 3 pairwise comparisons employing a Eonferroni adjustment ensure that the overall o: c: 0.05