Question

In order to examine the relationship between the selling price of a used car and its age, an analyst uses data from 20 recent transactions and estimates Price = β₀ + β₁Age + ε. A portion of the regression results is shown in the accompanying table. [You may find it useful to reference the t table.]

	Coefficients	Standard Error	t Stat	p-value
Intercept	21,241.95	738.41	28.767	1.68E-16
Age	−1,206.24	129.93		2.77E-08

a. Specify the competing hypotheses in order to determine whether the selling price of a used car and its age are linearly related.

• H₀: β₁ ≥ 0; H_A: β₁ < 0

• H₀: β₁ = 0; H_A: β₁ ≠ 0

• H₀: β₁ ≤ 0; H_A: β₁ > 0

b. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

c-1. Find the p-value.

• p-value 0.10
• 0.05 p-value < 0.10
• 0.02 p-value < 0.05
• 0.01 p-value < 0.02

• p-value < 0.01

c-2. At the 10% significance level, is the age of a used car significant in explaining its selling price?

d-1. Conduct a hypothesis test at the 10% significance level in order to determine if β₁ differs from −1,000. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

d-2. Find the p-value.

• 0.05 p-value < 0.10
• 0.02 p-value < 0.05
• 0.01 p-value < 0.02

• p-value < 0.01

• p-value 0.10

d-3. What is the conclusion to the test?

Answer 1