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A High School Counselor Was Interested in Finding Out How

question 18

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A high school counselor was interested in finding out how well student grade point averages (GPA) predict ACT scores.
A sample of the senior class data was reviewed to obtain GPA and ACT scores. The data are shown in the table, and regression output is given below.

$\begin{array}{|c|c|}\hline\text { GPA} & \text {ACT} \\\hline 3.25 & 24 \\\hline 2.87 & 21 \\\hline 2.66 & 18 \\\hline 3.33 & 22 \\\hline 2.87 & 22 \\\hline 3.21 & 22 \\\hline 2.76 & 18 \\\hline 3.91 & 28 \\\hline 3.55 & 29 \\\hline 2.55 & 18 \\\hline 2.44 & 20 \\\hline 3.22 & 24 \\\hline 3.01 & 21 \\\hline 3.44 & 24 \\\hline 3.22 & 25 \\\hline\end{array}$

$A high school counselor was interested in finding out how well student grade point averages (GPA) predict ACT scores. A sample of the senior class data was reviewed to obtain GPA and ACT scores. The data are shown in the table, and regression output is given below. \begin{array}{|c|c|} \hline\text { GPA} & \text {ACT} \\ \hline 3.25 & 24 \\ \hline 2.87 & 21 \\ \hline 2.66 & 18 \\ \hline 3.33 & 22 \\ \hline 2.87 & 22 \\ \hline 3.21 & 22 \\ \hline 2.76 & 18 \\ \hline 3.91 & 28 \\ \hline 3.55 & 29 \\ \hline 2.55 & 18 \\ \hline 2.44 & 20 \\ \hline 3.22 & 24 \\ \hline 3.01 & 21 \\ \hline 3.44 & 24 \\ \hline 3.22 & 25 \\ \hline \end{array} Dependent variable is: \quad \mathrm{ACT} No Selector \mathrm{R} squared =78.1 \% \quad \mathrm{R} squared (adjusted) =76.4 \% s=1.630 with 15-2=13 degrees of freedom \begin{array}{llrcc}\text { Source } & \text { Sum of Squares } & \text { df } & \text { Mean Square } & \text { F-ratio } \\ \text { Regression } & 123.041 & 1 & 123.041 & 46.3 \\ \text { Residual } & 34.5589 & 13 & 2.65838 & \\ & & & & \\\\ \text { Variable } & \text { Coefficient } & \text { s.e. of Coeff } & \text { t-ratio } & \text { prob } \\ \text { Constant } & -0.427035 & 3.382 & -0.126 & 0.9014 \\ \text { GPA } & 7.39697 & 1.087 & 6.80 & \leq 0.0001\end{array} -Is there evidence of an association between GPA and ACT score? Test an appropriate hypothesis and state your conclusion in the proper context.$
Dependent variable is: $\quad \mathrm{ACT}$
No Selector
$\mathrm{R}$ squared $=78.1 \% \quad \mathrm{R}$ squared (adjusted) $=76.4 \%$
$s=1.630$ with $15-2=13$ degrees of freedom
$\begin{array}{llrcc}\text { Source } & \text { Sum of Squares } & \text { df } & \text { Mean Square } & \text { F-ratio } \\ \text { Regression } & 123.041 & 1 & 123.041 & 46.3 \\ \text { Residual } & 34.5589 & 13 & 2.65838 & \\ & & & & \\\\ \text { Variable } & \text { Coefficient } & \text { s.e. of Coeff } & \text { t-ratio } & \text { prob } \\ \text { Constant } & -0.427035 & 3.382 & -0.126 & 0.9014 \\ \text { GPA } & 7.39697 & 1.087 & 6.80 & \leq 0.0001\end{array}$

-Is there evidence of an association between GPA and ACT score? Test an appropriate hypothesis and state your conclusion in the proper context.

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