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:

Nash Equilibrium

A concept within game theory where no participant can gain by unilaterally changing their strategy if the strategies of the others remain unchanged.

Optimal Strategy

The best or most efficient course of action to achieve a specific goal or maximize a particular set of outcomes under given conditions.

Nash Equilibrium

A concept in game theory where no player can benefit by changing strategies if the other players keep their strategies unchanged.

Nash Equilibrium

A concept in game theory where each player's strategy is optimal given the strategies of all other players, indicating a stable state from which no player has the incentive to deviate unilaterally.