New Car: Negotiating Price

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New Car: Negotiating Price  Suppose you are interested in buying a new Lincoln Navigator or Town Car. You are standing on the sales lot looking at a model with different options. The list price is on the vehicle. As a salesperson approaches, you wonder what the dealer invoice price is for this model with its options. The following data are based on information taken from Consumer Guide (Vol. 677). Let x be the list price (in thousands of dollars) for a random selection of these cars of different models and options. Let y be the dealer invoice (in thousands of dollars) for the given vehicle.

x

32.1

33.5

36.1

44

47.8

y

29.8

31.1

32

42.1

42.2

(a) Verify that Σx = 193.5, Σy = 177.2, Σx2= 7676.71, Σy2= 6432.5, Σxy = 7023.19, and r ≈ 0.977.

(b) Use a 1% level of significance to test the claim that ρ > 0.

(c) Verify that Se≈ 1.5223, a ≈ 1.4084, and b ≈ 0.8794.

(d) Find the predicted dealer invoice when the list price is x = 40(thousanddollars).

(e) Find a 95% confidence interval for y when x = 40 (thousand dollars).

(f) Use a 1% level of significance to test the claim that β > 0.

(g) Find a 90% confidence interval for β and interpret its meaning.