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Consider the data:
xᵢ: 2, 6, 9, 13, 20
yᵢ: 5, 19, 9, 25, 24
(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 = 0.05. 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
H ₀: 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.
A. Reject H₀. We cannot conclude that the relationship between x and y is significant.
B. Do not reject H₀. We conclude that the relationship between x and y is significant.
C. Do not reject H₀. We cannot conclude that the relationship between x and y is significant.
D. 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 = 0.05. State the null and alternative hypotheses.
H₀: β₁ ≠ 0
Ha: β₁ = 0
H₀: β₁ ≥ 0
Hₐ: β₁ < 0
H₀: β₁ = 0
Hₐ: β₁ ≠ 0
H₀: β₀ = 0
Hₐ: β₀ ≠ 0
H₀: β₀ ≠ 0
Hₐ: β ₀ = 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?
A. Reject H₀. We cannot conclude that the relationship between x and y is significant.
B. Do not reject H₀. We conclude that the relationship between x and y is significant.
C. Reject H₀. We conclude that the relationship between x and y is significant.
D. Do not reject H₀. We cannot conclude that the relationship between x and y is significant.

Sagot :

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