Please use SAS to solve if possible. Thanks!

QUESTION 1. (20 marks] In the first phase of a study of the expenditure of transporting astronauts via Elon Musk's Spacex space program versus NASA's space program was surveyed. Expenditure data on X, = fuel, X, = repair, and X; = capital expenditure in billions of dollars, were all measured on a per-1000 mile basis, for m = 36 Elon Musk and na = 23 NASA trips. The survey gave sample mean vectors (in billions of dollars) of [12.219] [10.106 f1 = 8.113 10.762 9.590 18.168 The survey data gave the 2 sample variance-covariance matrices as, 223.0134 12.3664 2.9066 4.3623 0.7599 2.3621 5, = 12 3664 17.5441 4.7731 : $2 = 0.7599 25.0512 7.6857 2.9066 47731 13.9633] 2.3621 7.6857 46.6543 The following pooled variance covariance matrix Spooks and associated inverse were also reported as follows, 15 0112 7.8550 2.6959 Spooked = 7.8550 20.7458 5.0960 2.6959 5.8960 26.5750 1.0939 -0.4084 -0.0203 [(=+4) Spooked] = -0.4084 0.8745 -0.1525 -0.0203 -0.1525 0.5640 *] Test for differences in the mean cost vectors. Set a = 0.05. State your null hypothesis and carry out the appropriate T' test using Spooked. Use the appropriate Fass critical value. (4 marks) b) Did you reject He 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] c) Construct the 95%% simultaneous confidence intervals for the pairs of mean components Haj - Ha for j = 1,2,3. [4 marks) d) Which costs, if any, appear to be quite different? (1 mark) el How is the pooled sample variance covariance matrix, Specks calculated from S, and S,7 Give the mathematical equation. (1 mark] f) Comment on the validity of the assumption that Is = Is used in the above analysis. (1 mark) gl Use the large sample variant of the T' test assuming unequal population variance covariance matrices, i.e. In = Ex to carry out the test of Mo. Use the appropriate y' critical value. (4 marks) h) Did you reject Hein part g) above? Justify your answer. (2 marks] Critical values of F distribution (you choose the correct one): Fass[0.10] = 2.18 Fass[0.05) = 2.76 Fa.sx [0.025] = 3.34 Fax[0.01] = 4.13