TABLE 13-8
It Is Believed That GPA (Grade Point

question 30

Multiple Choice

TABLE 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 from regressing GPA on ACT scores using a data set of 8 randomly chosen students from a Big-Ten university.
$$\begin{array}{l}\text { Regressing GPA on } \mathrm { ACT }\\\begin{array} { l c } \hline & \text { Regression Statistics } \\\hline \text { Multiple R } & 0.7598 \\\text { R Square } & 0.5774 \\\text { Adjusted R Square } & 0.5069 \\\text { Standard E rror } & 0.2691 \\\text { Observations } & 8\end{array}\end{array}$$

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

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

-Referring to Table 13-8, what are the decision and conclusion on testing whether there is any linear relationship at 1% level of significance between GPA and ACT scores?

• A) Do not reject the null hypothesis; hence there is sufficient evidence to show that ACT scores and GPA are linearly related.
• B) Reject the null hypothesis; hence there is not sufficient evidence to show that ACT scores and GPA are linearly related.
• C) Reject the null hypothesis; hence there is sufficient evidence to show that ACT scores and GPA are linearly related.
• D) Do not reject the null hypothesis; hence there is not sufficient evidence to show that ACT scores and GPA are linearly related.

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