SCENARIO 17-8
the Superintendent of a School District Wanted to Predict

SCENARIO 17-8
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), daily mean of the percentage of students attending class (% Attendance), mean teacher
salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in
the state. Following is the multiple regression output with $Y = \%$ Passing as the dependent variable, $X _ { 1 } = \%$ Attendance, $X _ { 2 } =$ Salaries and $X _ { 3 } =$ Spending:

$\begin{array}{lr}\hline{\text { Regression Statistics }} \\\hline \text { Multiple R } & 0.7930 \\\text { R Square } & 0.6288 \\\text { Adjusted R } & 0.6029 \\\text { Square } & \\\text { Standard } & 10.4570 \\\text { Error } & \\\text { Observations } & 47 \\\hline\end{array}$

ANOVA


$\begin{array}{lrrrrrr}\hline & \text { Coefficients } & \begin{array}{c}\text { Standard } \\\text { Error }\end{array} & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -753.4225 & 101.1149 & -7.4511 & 0.0000 & -957.3401 & -549.5050 \\\text { \% Attendance } & 8.5014 & 1.0771 & 7.8929 & 0.0000 & 6.3292 & 10.6735 \\\text { Salary } & 0.000000685 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\\text { Spending } & 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \\\hline\end{array}$
-Referring to Scenario 17-8, which of the following is the correct alternative hypothesis to determine whether there is a significant relationship between percentage of students passing the
Proficiency test and the entire set of explanatory variables? a) $H _ { 1 } : \beta _ { 0 } = \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } \neq 0$
b) $H _ { 1 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } \neq 0$
c) $H _ { 1 }$ : At least one of $\beta _ { j } \neq 0$ for $j = 0,1,2,3$
d) $H _ { 1 }$ : At least one of $\beta _ { j } \neq 0$ for $j = 1,2,3$

Correct Answer:

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