Question

Consider the data.

xi	2	6	9	13	20
yi	6	19	10	25	23

(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: β₁ = 0
H_a: β₁ ≠ 0H₀: β₀ = 0
H_a: β₀ ≠ 0    H₀: β₁ ≠ 0
H_a: β₁ = 0H₀: β₀ ≠ 0
H_a: β₀ = 0H₀: β₁ ≥ 0
H_a: 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 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.Reject H₀. We cannot 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: β₀ = 0
H_a: β₀ ≠ 0H₀: β₁ = 0
H_a: β₁ ≠ 0    H₀: β₀ ≠ 0
H_a: β₀ = 0H₀: β₁ ≠ 0
H_a: β₁ = 0H₀: β₁ ≥ 0
H_a: 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 =

What is your conclusion?

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.    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.

Answer 1

The statistical software output for this problem is:

Hence,

a) Standard error = 6.306

b) Hypotheses: H₀: β₁ = 0
H_a: β₁ ≠ 0

Test statistic = 1.967

p - Value = 0.1438

Conclusion: Do not reject H₀. We cannot conclude that the relationship between x and y is significant.

c) Hypotheses: H₀: β₁ = 0
H_a: β₁ ≠ 0

Test statistic = 3.87

p - Value = 0.1438

Conclusion: Do not reject H₀. We cannot conclude that the relationship between x and y is significant.