The summary statistics for a certain set of points are: $n = 23 , s _ { \mathrm { e } } = 2.302 , \sum ( x - \bar { x } ) ^ { 2 } = 15.372$, and $b _ { 1 } = 1.902$. Assume the conditions of the linear model hold. A $99 \%$ confidence interval for $\beta _ { 1 }$ will be constructed. How many degrees of freedom are there for the critical value?
A) 22
B) 23
C) 21
D) 24

Question

Quizplus · Accepted Answer

The critical value for a t-distribution with 21 degrees of freedom and a $99 \%$ confidence level is used to construct a confidence interval for $\beta _{1}$. The degrees of freedom for the critical value is equal to $n-2$ where $n$ is the sample size. Therefore, in this case $n-2=23-2=21$, so the answer is C: 21.

The Summary Statistics for a Certain Set of Points Are n=23,se=2.302,∑(x−xˉ)2=15.372n = 23 , s _ { \mathrm { e } } = 2.302 , \sum ( x - \bar { x } ) ^ { 2 } = 15.372n=23,se​=2.302,∑(x−xˉ)2=15.372

The Summary Statistics for a Certain Set of Points Are $n = 23 , s _ { \mathrm { e } } = 2.302 , \sum ( x - \bar { x } ) ^ { 2 } = 15.372$