Answer all questions below correctly.,,,

1. Julia recently received a GPS navigation system. (a) To test the accuracy of the GPS, she records her velocity at various times during her commute to work, then compares this information with the GPS's distance estimate. Let v() be Julia's velocity, in miles per hour (mi/h), at time t hours (h) after she begins driving to work. Julia records several values of v(t) in the following table. t (h) 0.06 0.11 0.16 0.21 0.26 v(t) (mi/h) 60 59 56 55 50 During Julia's drive, the car is always decelerating. i. Use a left Riemann sum with four equal subintervals to estimate the distance Julia traveled between =0.06 h and t = 0.26 h. ii. Is your estimate from part (a) an overestimate or an underestimate? ifi. Julia's GPS estimates that between ME Quote a p-value. b. Verify the equal variance assumption. Quote a p-value. V. (10 pts) The yield of a chemical process is related to the concentration of the reactant (3 levels) and the operating temperature (2 levels). A factorial experiment has been conducted with the results shown below. Temperature Concentration 150 F 81, 83. 79. 76 83, 85, 84, 81 89, 86, 88. 90 180"F 85, 86, 82, 80 83, 88. 85, 88 81. 78, 82, 79 Conduct an analysis of variance on this experiment including the two factors and their interaction. State appropriate hypotheses and draw your conclusions based on an a of 0.05. b. What are your recommendations regarding the concentration of the reactant and the operating temperature if high yield is desired? (Construct necessary interaction/main effect plots to support your answer) VI. (20 pts) Parts manufactured by an injection molding process are subjected to a compressive strength test. Data are given on the following 15 samples of five observations each. Sample No. 65.9 78 2 69 8 686 80.4 839 78 5 796 71.0 81.6 71.A 78. 1