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 6,250
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
Ha: β0 ≠ 0

H0: β0 ≠ 0
Ha: β0 = 0

H0: β1 ≠ 0
Ha: β1 = 0

H0: β1 ≥ 0
Ha: β1 < 0

H0: β1 = 0
Ha: β1 ≠ 0

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

p-value =

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.

The statistical software output for this problem is :

H0: β1 = 0
Ha: β1 ≠ 0

Test statistics = 52.33

P-value = 0.000

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

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