Refer to Exercise 11.3.a Do the data present sufficient

Chapter 11, Problem 23E

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QUESTION:

Refer to Exercise 11.3.

a Do the data present sufficient evidence to indicate that the slope \(\beta_{1}\) differs from zero? (Test at the 5% significance level.)

b What can be said about the attained significance level associated with the test implemented in part (a) using a table in the appendix?

c Applet Exercise What can be said about the attained significance level associated with the test implemented in part (a) using the appropriate applet?

d Find a 95% confidence interval for \(\beta_{1}\).

Equation transcription:

Text transcription:

beta{1}

Questions & Answers

QUESTION:

Refer to Exercise 11.3.

a Do the data present sufficient evidence to indicate that the slope \(\beta_{1}\) differs from zero? (Test at the 5% significance level.)

b What can be said about the attained significance level associated with the test implemented in part (a) using a table in the appendix?

c Applet Exercise What can be said about the attained significance level associated with the test implemented in part (a) using the appropriate applet?

d Find a 95% confidence interval for \(\beta_{1}\).

Equation transcription:

Text transcription:

beta{1}

ANSWER:

Step 1 of 6

(a)

In this part we need to test the null hypothesis

against the alternative hypothesis

with the significance level of .

The test statistic that we use for this test is:

where

where

where

and  is the number of data.

For this test statistic, the reject region is:

where

when  is a Student's -distribution with  degrees of freedom.

because of the symmetry of a Student's -distribution.

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