Question

Consider the following data on x = weight (pounds) and y = price (\$) for 10...

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
Ha: β0 ≠ 0

(b) H0: β1 ≠ 0
Ha: β1 = 0

(c) H0: β0 ≠ 0
Ha: β0 = 0

(d) H0: β1 ≥ 0
Ha: β1 < 0

(e)H0: β1 = 0
Ha: β1 ≠ 0

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

p-value =

(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.

The statistic software output for this problem is :

(a)

(e)

H0: β1 = 0
Ha: 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.