The summary statistics for a certain set of points are: $n = 18 , s _ { \mathrm { e } } = 8.078 , \sum ( x - \bar { x } ) ^ { 2 } = 7.614$ , and $b _ { 1 } = 1.29$ Assume the conditions of the linear model hold. A 99% confidence interval for $\beta _ { 1 }$ will be constructed.
Test the null hypothesis $H _ { 0 } : \beta _ { 1 } = 0$ versus $H _ { 0 } : \beta _ { 1 } > 0$ . Use the $\alpha = 0.01$ level of significance.

Question

The summary statistics for a certain set of points are:

n = 18 , s _ { \mathrm { e } } = 8.078 , \sum ( x - \bar { x } ) ^ { 2 } = 7.614

, and

b _ { 1 } = 1.29

Assume the conditions of the linear model hold. A 99% confidence interval for

\beta _ { 1 }

will be constructed.
Test the null hypothesis

H _ { 0 } : \beta _ { 1 } = 0

versus

H _ { 0 } : \beta _ { 1 } > 0

. Use the

\alpha = 0.01

level of significance.

Quizplus · Accepted Answer

The summary statistics provided do not include a test statistic or p-value directly related to testing the hypothesis about $\beta_1$. Without these or additional information (like the standard error of $\beta_1$), we cannot conclusively reject or fail to reject the null hypothesis based on the information given.

The Summary Statistics for a Certain Set of Points Are n=18,se=8.078,∑(x−xˉ)2=7.614n = 18 , s _ { \mathrm { e } } = 8.078 , \sum ( x - \bar { x } ) ^ { 2 } = 7.614n=18,se​=8.078,∑(x−xˉ)2=7.614

The Summary Statistics for a Certain Set of Points Are $n = 18 , s _ { \mathrm { e } } = 8.078 , \sum ( x - \bar { x } ) ^ { 2 } = 7.614$