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 X1 = fuel, X, = repair, and X3 = capital expenditure in billions of dollars, were all measured on a per-1000 mile basis, for n = 36 Elon Musk and nz = 23 NASA trips. The survey gave sample mean vectors (in billions of dollars) of 12.219] 10.106] 11= 8.113 3812 = 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 SI = 12.3664 17.5441 4.7731 ; $2 = 0.7599 25.8512 7.6857 2.9066 4.7731 13.9633] 2.3621 7.6857 46.6543] The following pooled variance covariance matrix Spooked and associated inverse were also reported as follows, 15.8112 7.8550 2.6959 Spooled = 7.8550 20.7458 5.8960 2.6959 5.8960 26.5750 1.0939 -0.4084 -0.02031 [(, +4) Spooked ]"= -0.4084 0.8745 -0.1525 -0.0203 -0.1525 0.5640 a) 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 Ho 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