Question

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

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
Ha: β0 ≠ 0

b) H0: β1 = 0
Ha: β1 ≠ 0    

c) H0: β1 ≥ 0
Ha: β1 < 0

d) H0: β0 ≠ 0
Ha: β0 = 0

e) H0: 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) 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
Ha: β0 ≠ 0

b)H0: β1 ≠ 0
Ha: β1 = 0    

c) H0: β1 ≥ 0
Ha: β1 < 0

d) H0: β1 = 0
Ha: β1 ≠ 0

e) H0: 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?

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.

Homework Answers

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
Ha: 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
Ha: 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.     

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