In testing $H _ { 0 } : \beta _ { 1 } = 0$ versus $H _ { \pm } : \beta _ { 1 } \neq 0$ using a sample of 20 observations, the rejection region for .01 level of significance test is
A) t $\geq$
-2)878
B) t $\leq$
2)878
C) -2.878 $\leq$
T $\leq$
2)878
D) either t $\geq$
2)878 or t $\leq$
-2)878
E) t = 0

Question

Quizplus · Accepted Answer

The correct answer is D because for a two-tailed test (indicated by $H _ { \pm } : \beta _ { 1 } \neq 0$), the rejection region is in both tails of the distribution. This means we reject $H_0$ if the test statistic is either significantly large (greater than a positive critical value) or significantly small (less than a negative critical value). The given critical value of ±2.878 corresponds to the tails of the t-distribution for a .01 level of significance with a sample size of 20 (which implies 19 degrees of freedom).

In Testing H0:β1=0H _ { 0 } : \beta _ { 1 } = 0H0​:β1​=0

In Testing $H _ { 0 } : \beta _ { 1 } = 0$