The Summary Statistics for a Certain Set of Points Are $n = 12 , s _ { \mathrm { e } } = 3.505 , \quad \sum ( x - \bar { x } ) ^ { 2 } = 14.353$

Multiple Choice

The summary statistics for a certain set of points are: $n = 12 , s _ { \mathrm { e } } = 3.505 , \quad \sum ( x - \bar { x } ) ^ { 2 } = 14.353$ , and $b _ { 1 } = 1.560$ Assume the conditions of the linear model hold. A 95% confidence interval for $\beta _ { 1 }$ will be constructed.
Construct the 95% confidence interval.

A) $- 0.1164 < \beta _ { 1 } < 3.2364$
B) $- 0.4763 < \beta _ { 1 } < 3.5963$
C) $- 0.1016 < \beta _ { 1 } < 3.5963$
D) $- 0.5013 < \beta _ { 1 } < 3.6213$