What is the margin of error? The summary statistics for a certain set of points are: $n = 18 , s _ { \mathrm { e } } = 2.127$,
$\sum ( x - \bar { x } ) ^ { 2 } = 13.384$, and $b _ { 1 } = 1.376$. Assume the conditions of the linear model hold. A $95 \%$ confidence interval for $\beta _ { 1 }$ will be constructed.
A)28.374080
B)1.011635
C)1.226753
D)1.232567

Question

Quizplus · Accepted Answer

The margin of error is given by $t_{\alpha/2, n-2} \times s_e \times \sqrt{\frac{1}{n} + \frac{(x-\bar{x})^2}{\sum(x-\bar{x})^2}}$. Plugging in the given values, we get $t_{0.025, 16} \times 2.127 \times \sqrt{\frac{1}{18} + \frac{(x-\bar{x})^2}{13.384}} = 1.232567$.

What Is the Margin of Error? the Summary Statistics for a Certain