Question

You may need to use the appropriate technology to answer this question.

Consider the data.

xi	2	6	9	13	20
yi	5	19	8	28	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.

a) H₀: β₀ = 0
H_a: β₀ ≠ 0

b) H₀: β₁ = 0
H_a: β₁ ≠ 0    

c) H₀: β₁ ≥ 0
H_a: β₁ < 0

d) H₀: β₀ ≠ 0
H_a: β₀ = 0

e) H₀: 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.

a) Do not reject H₀. We conclude that the relationship between x and y is significant.

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

c) 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 α = 0.05.

State the null and alternative hypotheses.

a)H₀: β₀ = 0
H_a: β₀ ≠ 0

b)H₀: β₁ ≠ 0
H_a: β₁ = 0    

c) H₀: β₁ ≥ 0
H_a: β₁ < 0

d) H₀: β₁ = 0
H_a: β₁ ≠ 0

e) H₀: β₀ ≠ 0
H_a: 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?

a) Reject H₀. We cannot conclude that the relationship between x and y is significant.

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

c) Do not reject H₀. We conclude that the relationship between x and y is significant.

d) Reject H₀. We conclude that the relationship between x and y is significant.

Answer 1

applying regression on above data from excel: data: data analysis:

a)

std error σ              =

=se =√s2=

8.066

b)

b) H₀: β₁ = 0
H_a: β₁ ≠ 0  

value of the test statistic=

(bo-β1)/se(β1)=

=

1.709

p value:

=

0.1860

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

c)

d) H₀: β₁ = 0
H_a: β₁ ≠ 0

value of the test statistic F =2.92

p-value =0.186

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