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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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Definitions:

Paradoxical Sleep

Another term for REM (Rapid Eye Movement) sleep, characterized by active brain patterns, dream occurrence, and temporary muscle paralysis.

Very Relaxed Muscles

A state of low tension in muscle fibers, often achieved through relaxation techniques, leading to reduced physical stress and strain.

Sleep Patterns

The natural cycle of various stages of sleep including REM and non-REM stages that repeats throughout the night.

Genetically Influenced

Traits or conditions that are shaped in part by genes inherited from one's parents.