Question 1 (35 pts). A pizza shop wants to price their pizzas according to a linear function P, = Bo+B1Ds, where Ds = diameter of the size s pizza. The cost to the shop to make each pizza is given in the following table: Size Small Medium Large X Large Diameter 8" 12" 16" 20 Cost $4 $9 $16 $25 Viewing net revenue on a pizza of size s as R3 = P, -C, = 2 +s, where C, is the cost to make the given pizza, the store wishes to choose Bo, Bi to minimize the sum (over the different sizes s) (Rs 2)? (a) (10 pts) What Bo, B, achieve the minimum value for this sum? (b) (5 pts) Suppose the shop wishes to have a special, with pricing Ps = B for any size s. What is the best choice of B to minimize [(R 2)2? (C) (10 pts) Conduct the test of hypothesis for distinguishing these models with a t-test, assuming the es are independent N (0,02) random variables. Do we reject the null hypothesis at the a = 0.05 level of significance? (d) (5 pts) Is the t-test appropriate in this setting? Why or why not? (e) (5 pts) Do the Gauss-Markov Conditions hold in this setting? Why or why not? Question 1 (35 pts). A pizza shop wants to price their pizzas according to a linear function P, = Bo+B1Ds, where Ds = diameter of the size s pizza. The cost to the shop to make each pizza is given in the following table: Size Small Medium Large X Large Diameter 8" 12" 16" 20 Cost $4 $9 $16 $25 Viewing net revenue on a pizza of size s as R3 = P, -C, = 2 +s, where C, is the cost to make the given pizza, the store wishes to choose Bo, Bi to minimize the sum (over the different sizes s) (Rs 2)? (a) (10 pts) What Bo, B, achieve the minimum value for this sum? (b) (5 pts) Suppose the shop wishes to have a special, with pricing Ps = B for any size s. What is the best choice of B to minimize [(R 2)2? (C) (10 pts) Conduct the test of hypothesis for distinguishing these models with a t-test, assuming the es are independent N (0,02) random variables. Do we reject the null hypothesis at the a = 0.05 level of significance? (d) (5 pts) Is the t-test appropriate in this setting? Why or why not? (e) (5 pts) Do the Gauss-Markov Conditions hold in this setting? Why or why not