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 = ?0 + ?1 Age + ?. A portion of the regression results is shown in the accompanying table

	Coefficients	Standard Error	t Stat	p-value
Intercept	21,187.96	740.41	25.85	1.10E+15
Age	–1,207.22	127.93		2.45E+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: ?1 ? 0; HA: ?1 < 0 H0: ?1 = 0; HA: ?1 ? 0 H0: ?1 ? 0; HA: ?1 > 0

b.	Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

Test statistic

c-1.	At the 5% significance level, find the critical value(s). (Round your answer to 2 decimal places.)

Critical value(s)

±

c-2	At the 5% significance level, what is the conclusion to the test? Is the age of a used car significant in explaining its selling price?

(Click to select)YesNo, we (Click to select)cancannot conclude that the age of a used car is significant in explaining its selling price

d-1.	Conduct a hypothesis test at the 5% significance level in order to determine if ?1 differs from –2000. Show all of the relevant steps. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

Test statistic
Critical value	±

Answer 1

Given: 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

To test, the hypothesis is that the selling price of a used car and its age are linearly related at 5% significance level.

a) The null and alternative hypothesis is,

₀ : ₁

_a :1     

b) The t-test statistics is,

The t-test statistics is -9.44.

c-1) The t critical value for the 95% confidence is,

The sample size is small and two tailed test.Look in the column headed and the row headed in the t distribution table by using degree of freedom is,

d.f.= n-2

= 20-2

= 18

The t critical value for the 95% confidence is 2.101.

c2) Decision: The conclusion is that the t value corresponds to same statistics is fall in the critical region, so the null hypothesis is rejected at 5% level of significance.There is sufficient evidence to indicate that the selling price of a used car and its age are linearly related.The result is statistically significant.

d1) To test the hypothesis is that the selling price of a used car and its age are linearly related difference from -2000 at 5% significance level.

The null and alternative hypothesis is,

₀ : ₁

_a :1     

The t-test statistics is,

  

  

  

The t-test statistics is -9.44

The t critical value for the 95% confidence is,

The sample size is small and two tailed test . Look in the column headed and the  row headed in the t distribution table by using degree of freedom is,

d.f. = n-2

= 20-2

= 18

The t critical value for the 95% confidence is 2.101