Question

Suppose you run a regression of Y on X2 and X3. You obtain a 95% confidence interval for the coefficient of X2: CI = [20, 30]. Which of the following answers is correct? (there may be multiple correct answers)

The t statistic for the test of significance of 8 lies in the rejection region of the test at 5% significance.

The p-value for the test of significance of 8 is smaller than 5%.

The p-value for the test of significance of B is larger than 5%.

Thet statistic for the test of significance of 82 lies in the acceptance region of the test at 5% significance.

Answer 1

Correct answer is option d.

The t statistic for the test to determine whether or not B2 is significant falls inside the acceptability region of the test when the significance level is set at 5%.

 

The significance of the coefficient is evaluated using a statistic known as the t statistic. The significance of the coefficient is proportional to the size of the t statistic. The confidence interval can be thought of as a measurement of how precise an estimate of the coefficient can be. When referring to the confidence interval, the term "95%" indicates that there is a level of certainty that the true value of the coefficient will fall within the confidence interval 95% of the time.

 

The t statistic for the test to determine whether or not B2 is significant falls inside the acceptability region of the test when the significance level is set at 5%. This indicates that the p-value for the significance test of B2 is lower than 5% rather than being significantly higher.

Correct answer is option d.