In: Statistics and Probability
Consider the data.
xi |
2 | 6 | 9 | 13 | 20 |
---|---|---|---|---|---|
yi |
9 | 19 | 9 | 26 | 25 |
(a)
What is the value of the standard error of the estimate? (Round your answer to three decimal places.)
(b)
Test for a significant relationship by using the t test. Use α = 0.05.
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 three decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value =
State your conclusion.
Reject H0. We cannot conclude that the relationship between x and y is significant.Reject H0. We conclude that the relationship between x and y is significant. Do not reject H0. We cannot conclude that the relationship between x and y is significant.Do not reject H0. We conclude that the relationship between x and y is significant.
(c)
Use the F test to test for a significant relationship. Use α = 0.05.
State the null and alternative hypotheses.
H0: β1 = 0
Ha: β1 ≠
0H0: β1 ≥ 0
Ha: β1 <
0 H0:
β0 ≠ 0
Ha: β0 =
0H0: β1 ≠ 0
Ha: β1 =
0H0: β0 = 0
Ha: β0 ≠ 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 =
What is your conclusion?
Reject H0. We conclude that the relationship between x and y is significant.Reject H0. We cannot conclude that the relationship between x and y is significant. Do not reject H0. We conclude that the relationship between x and y is significant.Do not reject H0. We cannot conclude that the relationship between x and y is significant.