A Confidence Interval for the Slope $\beta _ { 1 }$

question 51

Multiple Choice

A confidence interval for the slope $\beta _ { 1 }$ for a regression line $\mathrm { y } = \beta _ { 0 } + \beta _ { 1 } \mathrm { x }$ can be found by evaluating the limits in $\mathrm { t }$ interval below:
$$\begin{array} { l } \mathrm { b } _ { 1 } - \mathrm { E } < \beta _ { 1 } < \mathrm { b } _ { 1 } + \mathrm { E } _ { g } \\\text { where } \mathrm { E } = \frac { \left( \mathrm { t } _ { \alpha / 2 } \right) \mathrm { se } _ { \mathrm { e } } } { \sqrt { \sum \mathrm { x } ^ { 2 } - \left( \sum \mathrm { x } \right) ^ { 2 } / \mathrm { n } } } .\end{array}$$
The critical value $t _ { \alpha / 2 }$ is found from the t-table using $\mathrm { n } - 2$ degrees of freedom and $\mathrm { b } _ { 1 }$ is calculated in the usual v from the sample data.
Use the data below to obtain a $95 \%$ confidence interval estimate of $\beta _ { 1 }$ .
$\begin{array}{c|ccccc}\mathrm{x} \text { (hours studied) } & 2.5 & 4.5 & 5.1 & 7.9 & 11.6 \\\hline \mathrm{y} \text { (score on test) } & 66 & 70 & 60 & 83 & 93\end{array}$

• A) \(0.322 < \beta _ { 1 } < 6.488\)
• B) \(1.936 < \beta _ { 1 } < 4.874\)
• C) \(0.134 < \beta _ { 1 } < 6.676\)
• D) \(0.686 < \beta _ { 1 } < 6.124\)

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