Solve the Problem $\beta _ { 1 }$ For a Regression Line

question 146

Multiple Choice

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

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

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