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 + β1 Age + ε. A portion of the regression results is shown in the accompanying table

	Coefficients	Standard Error	t Stat	p-value
Intercept	21,266.93	733.44	23.84	4.55E+15
Age	–1,201.23	128.96		2.46E+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; HA: β1 < 0 H0: β1 = 0; HA: β1 ≠ 0 H0: β1 ≤ 0; HA: β1 > 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 10% significance level, find the critical value(s). (Round your answer to 2 decimal places.)

Critical value(s)

±

c-2	At the 10% 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 10% significance level in order to determine if β1 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	±

d-2	What is the conclusion to the test?

(Click to select)Do not rejectReject H0, we (Click to select)cannotcan conclude that β1 ≠ –2,000.

Answer 1

Solution :-

Given data:

	Coefficients	Standard Error	t Stat	p-value
Intercept	21,266.93	733.44	23.84	4.55E+15
Age	–1,201.23	128.96		2.46E+08

( a ) :-

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

The null and alternative hypothesis are ;

i.e, second option is correct answer.

( b ) :-

Calculate the value of the test statistic.

From given data, Test statistic is ,

Test statistic = (–1,201.23) / 128.96

Test statistic = -9.3147

Test statistic is -9.34.

( c1 ) :-

At the 10% significance level, find the critical value(s)

we know that at 10% significance level,

Critical value is 1.645

Critical value is 1.64.

( c2 ) :-

At the 10% significance level, what is the conclusion to the test? Is the age of a used car significant in explaining its selling price?

From above parts, Critical value is greater than Test statistic.

we can conclude that as, Yes, we can conclude that the age of a used car is significant in explaining its selling price

( d1 ) :-

Conduct a hypothesis test at the 10% significance level in order to determine if β₁ differs from –2000. Show all of the relevant steps.

From given data, Test statistic is ,

Test statistic = [ –1,201.23-(-2000) ]/ 128.96

Test statistic = 798.77 / 128.96

Test statistic = 6.1939

  Test statistic = 6.19.

we know that at 10% significance level,

Critical value is 1.645

Critical value is 1.64.

( d2 ) :-

What is the conclusion to the test?

We can conclude that as, Reject H₀, we can conclude that β₁ ≠ –2,000.