3) A company produces lugc sleds2 with steal runners along the bottom of the sled {c.g., like the blades on a skate). They coat the runners with a solution to prevent them from rusting. A new solution is under development and was studied by making 5 runs on the luge and 5 runs with the old solution. The following rounded speeds {in mph) for the lugc were recorded: Old Solution 73 \"I4 85 3'8 83 ---au ' MacKay, R. J.. & Oldford, R. W. (2000) Scientic method, statistical method and the speed of light. Statistical Science, 2542?8. I https:Hadventure.howsm'works.comfoutdooract'ivitiesfsansportsfhigelhhn a. Using R, produce a high-quality (i.c., with a title, labels on axes, etc.) graph to compare the two solutions. i. Explain your choice of graph (i.e., Why did you choose it?). ii. Interpret the results from the graph. b. Do the results indicate that the new solution results in faster luge speeds than the old solution? Assume that the variances for the two solutions are unequal. i. State the hypotheses we wish to test. ii. Perform the test using a critical region at a 5% significance level. State your conclusions. iii. Perform the mt using a 95% condence interval. State your conclusions. iv. Compare the results in (ii) and (iii)