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	6,250
C	14.9	8,370
D	15.9	6,200
E	17.2	4,000
F	13.1	8,600
G	16.2	6,000
H	17.1	2,680
I	17.6	3,400
J	14.1	8,000

These data provided the estimated regression equation

ŷ = 28,503 − 1,434x.

For these data, SSE = 6,833,947.38 and SST = 51,535,800. Use the F test to determine whether the weight for a bike and the price are related at the 0.05 level of significance.

State the null and alternative hypotheses.

H₀: β₀ = 0
H_a: β₀ ≠ 0

H₀: β₀ ≠ 0
H_a: β₀ = 0

H₀: β₁ ≠ 0
H_a: β₁ = 0

H₀: β₁ ≥ 0
H_a: β₁ < 0

H₀: β₁ = 0
H_a: β₁ ≠ 0

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

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

p-value =

State your conclusion.

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

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

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

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

Answer 1

The statistical software output for this problem is :

H₀: β₁ = 0
H_a: β₁ ≠ 0

Test statistics = 52.33

P-value = 0.000

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