Question

Suppose you are interested in buying a new Toyota Corolla. 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 a random selection of Toyota Corollas of different models and options. Let y be the dealer invoice (in thousands of dollars) for the given vehicle. x 12.9 13.3 12.8 13.6 13.4 14.2 y 11.8 11.7 11.5 12.2 12.0 12.8

(a) Verify that Σx = 80.2, Σy = 72, Σx2 = 1073.3, Σy2 = 865.06, Σxy = 963.51, and r ≈ 0.948. Σx Σy Σx2 Σy2 Σxy r

(b) Use a 1% level of significance to test the claim that ρ > 0. (Use 2 decimal places.) t critical t

(c) Verify that Se ≈ 0.1638, a ≈ 0.528, and b ≈ 0.858. Se a b

(d) Find the predicted dealer invoice when the list price is x = 13.1 (thousand dollars). (Use 2 decimal places.)

(e) Find a 90% confidence interval for y when x = 13.1 (thousand dollars). (Use 2 decimal places.) lower limit upper limit

(f) Use a 1% level of significance to test the claim that β > 0. (Use 2 decimal places.) t critical t

(g) Find a 90% confidence interval for β and interpret its meaning. (Use 2 decimal places.) lower limit upper limit

Answer 1