Question

The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and it selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.

Car	Age (Years)	Selling Price ($000)
1	9	8.1
2	7	6.0
3	11	3.6
4	12	4.0
5	8	5.0
6	7	10.0
7	8	7.6
8	11	8.0
9	10	8.0
10	12	6.0
11	6	8.6
12	6	8.0

The regression equation is Ŷ=11.18-0.49X, the sample size is 12 and the standard error of the slope is 0.23. Use the .05 significance level. Can we conclude that the slope of the regression line is less than zero?

(NEED ALL THE WORKINGS AND STEP)

Answer 1

Solution:

Given:

The regression equation is Ŷ=11.18-0.49X,

Thus slope = b₁ = -0.49

the sample size is 12 and

the standard error of the slope = S_b1 =  0.23.

Significance level = 0.05

We have to test if the slope of the regression line is less than zero

Step 1) State H0 and H1:

Vs

  

( Left tailed test, that is one tailed)

Step 2) Test statistic:

Step 3) Find t critical value:

df = n -2 = 12-2 = 10

Significance level = 0.05

Look in t table for df = 10 and one tail area = 0.05 and find t critical value

t critical value = 1.812

since this is left tailed test , t critical value is negative.

thus t critical value = -1.812

Step 4) Decision Rule:
Reject null hypothesis H0, if t test statistic value < t critical value = -1.812 , otherwise we fail to reject H0

Since t test statistic value = -2.130 < t critical value = -1.812, we reject null hypothesis H0.

Step 5) Conclusion:

At 0.05 significance level , there is sufficient evidence to conclude that  the slope of the regression line is less than zero