Question

# Consider the data. xi 2 6 9 13 20 yi 5 16 8 24 23 (a)...

Consider the data.

 xi yi 2 6 9 13 20 5 16 8 24 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: β0 ≠ 0
Ha: β0 = 0

H0: β1 ≠ 0
Ha: β1 = 0

H0: β1 = 0
Ha: β1 ≠ 0

H0: β0 = 0
Ha: β0 ≠ 0

H0: β1 ≥ 0
Ha: β1 < 0

Find the value of the test statistic. (Round your answer to three decimal places.)

p-value =

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.

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.

(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 ≠ 0

H0: β1 ≥ 0
Ha: β1 < 0

H0: β0 = 0
Ha: β0 ≠ 0

H0: β0 ≠ 0
Ha: β0 = 0

H0: β1 ≠ 0
Ha: β1 = 0

Find the value of the test statistic. (Round your answer to two decimal places.)

p-value =

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.

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.

Using Excel, go to Data, select Data Analysis, choose Regression.

 SUMMARY OUTPUT Regression Statistics Multiple R 0.803 R Square 0.645 Adjusted R Square 0.526 Standard Error 5.910 Observations 5 ANOVA df SS MS F Significance F Regression 1 190 190.000 5.439 0.1019 Residual 3 104.8 34.933 Total 4 294.8 Coefficients Standard Error t Stat P-value Intercept 5.2 5.037 1.032 0.3778 X 1 0.429 2.332 0.1019

a) Standard error = 5.910

b) H0: β1 = 0
Ha: β1 ≠ 0

Test statistic = 2.332

p-value = 0.1019

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

c) H0: β1 = 0
Ha: β1 ≠ 0

Test statistic = 5.44

p-value = 0.102

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

#### Earn Coins

Coins can be redeemed for fabulous gifts.