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) \(28.10 < \beta _ { 0 } < 77.66\)

---

Definitions:

FUTA Tax Return

A federal tax form required from employers to report and pay unemployment taxes to the Internal Revenue Service, associated with the Federal Unemployment Tax Act.

Wage And Tax Statement

A form, typically referred to as a W-2 form in the United States, that employers provide to employees detailing the employee's annual wages and the amount of taxes withheld from their paycheck.

Tax Liability Accounts

Financial accounts that track the amount of tax that a person or organization owes to the government.

General Checking Account

A type of bank account that allows for the deposit and withdrawal of funds for daily transactions.