A Confidence Interval for The $y$ -Intercept $\beta _ { 0 }$

question 113

Multiple Choice

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

• A) \(31.10 < \beta _ { 0 } < 74.66\)
• B) \(37.83 < \beta _ { 0 } < 67.93\)
• C) \(33.50 < \beta _ { 0 } < 72.26\)
• D) \(28.10 < \beta _ { 0 } < 77.66\)

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Definitions:

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The way group members deal with one another while working on a task.

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A phase in teamwork or project management where the group organizes its efforts and resources effectively to execute a plan.

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The stages that a group goes through from its formation to achieving high levels of performance and cohesion.

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Leaders who tend to delegate authority and confer with others in making decisions, but who makes the actual decisions independently.