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A College Admissions Counselor Was Interested in Finding Out How

question 7

Essay

A college admissions counselor was interested in finding out how well high school grade point averages (HS GPA) predict first-year college GPAs (FY GPA). A random sample of data from first-year students was reviewed to obtain high school and first-year college GPAs. The data are shown below: $\begin{array}{|l|l|l|l|l|l|l|l|l|}\hline \text {HS GPA }& 3.82 & 3.90 & 3.20 & 3.40 & 3.88 & 3.50 & 3.60 & 3.70 \\\hline \text {FY GPA} & 3.75 & 3.45 & 2.60 & 2.95 & 3.50 & 2.76 & 3.10 & 3.40 \\\hline\end{array}$

$\begin{array}{|c|c|c|c|c|c|c|c|c|}\hline\text { HS GPA} & 4.00 & 3.30 & 3.50 & 3.80 & 3.87 & 4.00 & 3.20 & 3.82 \\\hline\text { FY GPA }& 3.90 & 2.70 & 3.00 & 3.00 & 3.10 & 3.77 & 2.80 & 3.54 \\\hline\end{array}$

Dependent variable is: $\quad$ FY GPA
No Selector
$\mathrm{R}$ squared $=75.4 \% \quad \mathrm{R}$ squared (adjusted) $=73.6 \%$
$s=0.2118$ with $16-2=14$ degrees of freedom

$\begin{array}{llrrr}\text { Source } & \text { Sum of Squares } & \text { df } & \text { Mean Square } & \text { F-ratio } \\ \text { Regression } & 1.92283 & 1 & 1.92283 & 42.9 \\ \text { Residual } & 0.627867 & 14 & 0.044848 & \\ & & & & \\ \text { Variable } & \text { Coefticient } & \text { s.e. of Coeft } & \text { t-ratio } & \text { prob } \\ \text { Constant } & -1.56410 & 0.7306 & -2.14 & 0.0504 \\ \text { HS GPA } & 1.30527 & 0.1993 & 6.55 & \leq 0.0001\end{array}$

$A college admissions counselor was interested in finding out how well high school grade point averages (HS GPA) predict first-year college GPAs (FY GPA). A random sample of data from first-year students was reviewed to obtain high school and first-year college GPAs. The data are shown below: \begin{array}{|l|l|l|l|l|l|l|l|l|} \hline \text {HS GPA }& 3.82 & 3.90 & 3.20 & 3.40 & 3.88 & 3.50 & 3.60 & 3.70 \\ \hline \text {FY GPA} & 3.75 & 3.45 & 2.60 & 2.95 & 3.50 & 2.76 & 3.10 & 3.40 \\ \hline \end{array} \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline\text { HS GPA} & 4.00 & 3.30 & 3.50 & 3.80 & 3.87 & 4.00 & 3.20 & 3.82 \\ \hline\text { FY GPA }& 3.90 & 2.70 & 3.00 & 3.00 & 3.10 & 3.77 & 2.80 & 3.54 \\ \hline \end{array} Dependent variable is: \quad FY GPA No Selector \mathrm{R} squared =75.4 \% \quad \mathrm{R} squared (adjusted) =73.6 \% s=0.2118 with 16-2=14 degrees of freedom \begin{array}{llrrr}\text { Source } & \text { Sum of Squares } & \text { df } & \text { Mean Square } & \text { F-ratio } \\ \text { Regression } & 1.92283 & 1 & 1.92283 & 42.9 \\ \text { Residual } & 0.627867 & 14 & 0.044848 & \\ & & & & \\ \text { Variable } & \text { Coefticient } & \text { s.e. of Coeft } & \text { t-ratio } & \text { prob } \\ \text { Constant } & -1.56410 & 0.7306 & -2.14 & 0.0504 \\ \text { HS GPA } & 1.30527 & 0.1993 & 6.55 & \leq 0.0001\end{array} -Create and interpret a 95% confidence interval for the slope of the regression line.$
-Create and interpret a 95% confidence interval for the slope of the regression line.

Definitions:

Standard Normal Random Variable

A random variable with a mean of zero and a standard deviation of one, following the standard normal distribution, which is a specific instance of the normal distribution.

Average Balance

Average balance is a financial term referring to the sum of all balances during a certain period divided by the number of days in that period, often used in banking to assess fees or determine interest.

Standard Deviation

An evaluation of how spread out or dispersed a collection of data points is.

Normally Distributed

A data distribution pattern that follows the normal (bell curve) distribution.