SCENARIO 13-8
It Is Believed That GPA (Grade Point Average

question 76

Multiple Choice

SCENARIO 13-8
It is believed that GPA (grade point average, based on a four point scale) should have a positive linear
relationship with ACT scores. Given below is the Excel output for predicting GPA using ACT scores
based a data set of 8 randomly chosen students from a Big-Ten university. Regressing GPA on ACT
$\begin{array}{lr}\hline {\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7598 \\\text { R Square } & 0.5774 \\\text { Adjusted R Square } & 0.5069 \\\text { Standard Error } & 0.2691 \\\text { Observations } & 8\end{array}$

ANOVA
$\begin{array}{lcccccr} & d f &{\text { SS }} & M S & F & \text { Significance } F \\\hline \text { Regression } & 1 & 0.5940 & 0.5940 & 8.1986 & 0.0286 \\\text { Residual } & 6 & 0.4347 & 0.0724 & & \\\text { Total } & 7 & 1.0287 & &\end{array}$

$\begin{array}{lccccrr}\hline & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & 0.5681 & 0.9284 & 0.6119 & 0.5630 & -1.7036 & 2.8398 \\\text { ACT } & 0.1021 & 0.0356 & 2.8633 & 0.0286 & 0.0148 & 0.1895\end{array}$

-Referring to Scenario 13-8, the value of the measured (observed) test statistic of the F-test for $$H _ { 0 } : \beta _ { 1 } = 0 \text { vs. } H _ { 1 } : \beta _ { 1 } \neq 0$$

• A) may be negative.
• B) is always positive.
• C) is always negative.
• D) has the same sign as the corresponding t test statistic.

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