Question

Consider the following data on x = weight (pounds) and y = price ($) for 10 road-racing bikes.

Brand	Weight	Price ($)
A	17.8	2,100
B	16.1	6,350
C	14.9	8,370
D	15.9	6,200
E	17.2	4,000
F	13.1	8,500
G	16.2	6,000
H	17.1	2,680
I	17.6	3,500
J	14.1	8,000

These data provided the estimated regression equation  ŷ = 28,175 − 1,413x. For these data, SSE = 7,270,445.08 and SST = 50,662,800. Use the F test to determine whether the weight for a bike and the price are related at the 0.05 level of significance.

1. State the null and alternative hypotheses.

(a) H₀: β₀ = 0
H_a: β₀ ≠ 0

(b) H₀: β₁ ≠ 0
H_a: β₁ = 0    

(c) H₀: β₀ ≠ 0
H_a: β₀ = 0

(d) H₀: β₁ ≥ 0
H_a: β₁ < 0

(e)H₀: β₁ = 0
H_a: β₁ ≠ 0

2. Find the value of the test statistic. (Round your answer to two decimal places.)

3. Find the p-value. (Round your answer to three decimal places.)

p-value =

4.State your conclusion.

(a) Do not reject H₀. We cannot conclude that the relationship between weight (pounds) and price ($) is significant.

(b) Reject H₀. We cannot conclude that the relationship between weight (pounds) and price ($) is significant.     

(c) Reject H₀. We conclude that the relationship between weight (pounds) and price ($) is significant.

(d) Do not reject H₀. We conclude that the relationship between weight (pounds) and price ($) is significant.

Answer 1

The statistic software output for this problem is :

(a)

(e)

H₀: β₁ = 0
H_a: β₁ ≠ 0

Test statistics = -6.91

P-value = 0.000

(c) Reject H₀. We conclude that the relationship between weight (pounds) and price ($) is significant.