A Collection of Paired Data Consists of the Number of Years

question 100

Multiple Choice

A collection of paired data consists of the number of years that students have studied Spanish and their scores on a Spanish language proficiency test. A computer program was used to obtain the least squares linear regression line and the computer output is shown below. Along with the paired sample data, the program was also given an x value of 2 (years of study) to be used for predicting test score. The regression equation is
$\begin{array}{lcccc}{\text { Score }=31.55+10.90 \text { Years. }} \\\text { Predictor } & \text { Coef } & \text { StDev } & \text { T } & \text { P } \\\text { Constant } & 31.55 & 6.360 & 4.96 & 0.000 \\\text { Years } & 10.90 & 1.744 & 6.25 & 0.000\end{array}$
$$\mathrm{S}=5.651 \quad \mathrm{R}-\mathrm{Sq}=83.0 \% \quad \mathrm{R}-\mathrm{Sq}(\mathrm{Adj}) =82.7 \%$$
Predicted values
$\begin{array}{llcc}\text { Fit } & \text { StDev Fit } & 95.0 \% \text { CI } & 95.0 \% \text { PI } \\ 53.35 & 3.168 & (42.72,63.98) & (31.61,75.09) \end{array}$
For a person who studies for 2 years, obtain the $95 \%$ prediction interval and write a statement interpreting the in

• A) \( (42.72,63.98) \); We can be \( 95 \% \) confident that the mean test score of all individuals who study 2 years will lie in the interval \( (42.72,63.98) \)
• B) \( (31.61,75.09) \); We can be \( 95 \% \) confident that the test score of an individual who studies 2 years will lie in the interval \( (31.61,75.09) \)
• C) \( (31.61,75.09) \); We can be \( 95 \% \) confident that the mean test score of all individuals who study 2 years will lie in the interval \( (31.61,75.09) \)
• D) \( (42.72,63.98) \); We can be \( 95 \% \) confident that the test score of an individual who studies 2 years will lie in the interval \( (42.72 .63 .98) \)

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Definitions:

Optimal Capital Structure

The best mix of debt, preferred stock, and common equity that maximizes a company’s stock price while minimizing its cost of capital.

Stock Price

The current market price of a company's shares, as bought and sold by investors on stock exchanges.

Cost of Capital

The mandatory rate of gain a business must realize on its investment schemes to maintain its market identity and attract funds.

Return on Equity

A measure of financial performance calculated by dividing net income by shareholders' equity, indicating how efficiently equity is used to generate profits.