In: Statistics and Probability
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 | 8,500 |
G | 16.2 | 6,000 |
H | 17.1 | 2,580 |
I | 17.6 | 3,500 |
J | 14.1 | 8,000 |
These data provided the estimated regression equation
ŷ = 28,243 − 1,418x.
For these data, SSE = 7,368,713.71 and SST = 51,100,800. 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 =
0H0: β1 ≠ 0
Ha: β1 =
0 H0:
β0 = 0
Ha: β0 ≠
0H0: β1 = 0
Ha: β1 ≠
0H0: β1 ≥ 0
Ha: 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 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 ($) is significant.Reject H0. We conclude that the relationship between weight (pounds) and price ($) is significant.