SCENARIO 13-15
the Superintendent of a School District Wanted to Predict

question 72

Multiple Choice

SCENARIO 13-15
The superintendent of a school district wanted to predict the percentage of students passing a sixth- grade proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing) , mean teacher salary in thousands of dollars (Salaries) , and instructional spending per pupil in thousands of dollars (Spending) of 47 schools in the state.
Following is the multiple regression output with Y = % Passing as the dependent variable,
X1 =
Salaries and
X 2 = Spending: $$\begin{array}{l}\begin{array} { l r } \hline { \text { Regression Statistics } } \\\hline \text { Multiple R } & 0.4276 \\\text { R Square } & 0.1828 \\\text { Adjusted R Square } & 0.1457 \\\text { Standard Error } & 5.7351 \\\text { Observations } & 47 \\\hline\end{array}\\\\\text { ANOVA }\\\begin{array} { l r r r r r } \hline & d f & { \text { SS } } & { \text { MS } } & \text { F } & { \text { Significance } F } \\\hline \text { Regression } & 2 & 323.8284 & 161.9142 & 4.9227 & 0.0118 \\\text { Residual } & 44 & 1447.2094 & 32.8911 & & \\\text { Total } & 46 & 1771.0378 & & & \\\hline\end{array}\\\\\begin{array} { l r r r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & - 72.9916 & 45.9106 & - 1.5899 & 0.1190 & - 165.5184 & 19.5352 \\\text { Salary } & 2.7939 & 0.8974 & 3.1133 & 0.0032 & 0.9853 & 4.6025 \\\text { Spending } & 0.3742 & 0.9782 & 0.3825 & 0.7039 & - 1.5972 & 2.3455 \\\hline\end{array}\end{array}$$
-Referring to SCENARIO 13-15, which of the following is a correct statement?

• A)The mean percentage of students passing the proficiency test is estimated to go up by 2.79% when mean teacher salary increases by one thousand dollars.
• B)The mean teacher salary is estimated to go up by 2.79% when mean percentage of students passing the proficiency test increases by 1%.
• C)The mean percentage of students passing the proficiency test is estimated to go up by 2.79% when mean teacher salary increases by one thousand dollars holding constant the instructional spending per pupil.
• D)The mean teacher salary is estimated to go up by 2.79% when mean percentage of students passing the proficiency test increases by 1% holding constant the instructional spending per pupil.

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Definitions:

Standard Deviation

A measure of the dispersion or spread of a set of data from its mean value.

Process Distribution Mean

The average value or central tendency of a distribution for a process' outcomes over a period of time.

Common Variation

Variability in data that is shared among all observations or variables being studied.

Randomly Occurring

Randomly occurring refers to events or phenomena that happen without a predictable pattern, often analyzed in probability and statistics to understand patterns and occurrences in data.