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 information taken from Consumer Guide. Let x be the list price (in thousands of dollars) for 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.

Parts (a) and (b) relate to testing p. Part (c) requests the value of Se. Part (e) relates to confidence intervals for prediction. Part (f) relates to testing β.
Answers may vary due to rounding.
(a) Verify that ˆ‘x = 79.6, ˆ‘y = 72.1, ˆ‘x2 = 1057.76, ˆ‘y2 = 867.49, ˆ‘xy = 957.84, and r ‰ˆ 0.956.
(b) Use a 1% level of significance to test the claim that p > 0.
(c) Verify that Se ‰ˆ 0.1527, a ‰ˆ 1.965, and b ‰ˆ 0.758.
(d) Find the predicted dealer invoice when the list price is x = 14 (thousand dollars).
(e) Find an 85% confidence interval for y when x = 14 (thousand dollars).
(f) Use a 1% level of significance to test the claim that β > 0.

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