This is Multivariate Analysis question. Please solve it manually and SAS

Expenditure data on X1 = fuel, X2 = repair, and X3 = capital expenditure in billions of dollars, were all measured on a per-1000 mile basis, for n1 = 36 SpaceX and n2 = 23 NASA trips.

Rest of the question in

Q1_Part_1

Q1_Part_2

Q1_Part_3

in following attachments

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 variancecovariance matrices as, 51: 12.3664 17.5441 4.7731 0.7599 25.8512 7.6857 223.0134 12.3664 2.9066] [4.3623 0.7599 2.3621 I ; 52 = . 2.9066 4.7731 13.9633 2.3621 7.6857 46.6543 The following pooled variance covariance matrix Spooled 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 + 5 mm = 0.4084 0.8745 0.1525. T11 7'12 p 0.0203 0.1525 0.5640 Test for differences in the mean cost vectors. Set at = 0.05. State your null hypothesis and carry out the appropriate T;l 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 of the mean components most responsible for the rejection. (3 marks) Construct the 95% simultaneous confidence intervals for the pairs of mean components ulj [1.2ijij 1,2,3. (4 marks) Which costs, if any, appear to be quite different? (1 mark) How is the pooled sample variance covariance matrix, Spooied 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 Ho in 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