This is a Multivariate Analysis question

Expenditure data on X1 = fuel, X2 = repair, and X3 = capital expenditure in billions of dollars, were all measured on a per1000 mile basis, for n1 = 36 Elon Musk and n; = 23 NASA trips. The survey gave sample mean vectors (in billions of dollars) of 12.219 10.106 :21 = 8.113 ; 22 = 10.762 . 9.590 18.168 The survey data gave the 2 sample variance-covariance matrices as, 51: 12.3664 17.5441 4.7731 0.7599 25.8512 7.6857 223.0134- 123664 2.9066] [4.3623 0.7599 2.3621] ; 52 = . 2.9066 4.7731 13.9633 2.3621 7.6857 46.6543 The following pooled variance covariance matrix 5666168 and associated inverse were also reported as follows, 5 p 7.8550 20.7458 5.8960 [15.8112 7.8550 2.6959] ooled : 2.6959 5.8960 26.5750 1 1 _1 1.0939 0.4084 0.0203 + S 00\Test for differences in the mean cost vectors. Set (1 = 0.05. State your null hypothesis and carry out the appropriate T2 test using Spooled. Use the appropriate F355 critical value. (4 marks) Did you reject H0 in part a)? If the hypothesis of equal cost vectors was rejected, find the linear combination ofthe mean components most responsible for the rejection. (3 marks) Construct the 95% simultaneous confidence intervals for the pairs of mean components ulj - ugjforj = 1,2,3. (4 marks) Which costs, if any, appear to be quite different? (1 mark) How is the pooled sample variance covariance matrix, Spooled calculated from 51 and 52? Give the mathematical equation. (1 mark) f) Comment on the validity of the assumption that E1 = Ez used in the above analysis. (1 mark) g) Use the large sample variant of the T2 test assuming unequal population variance covariance matrices, i.e. Z1 # Z2, to carry out the test of Ho. Use the appropriate x2 critical value. (4 marks) h) Did you reject Hoin part g) above? Justify your answer. (2 marks) Critical values of F distribution (you choose the correct one): F3.55 F3,55(0.10) = 2.18 F3,55(0.05) = 2.76 F3,55(0.025) = 3.34 F3,55(0.01) = 4.13