A Statistics Professor Gave Three Quizzes Leading Up to the First

Essay

A statistics professor gave three quizzes leading up to the first test in his class. The quiz grades and test grade for each of eight students are given in the table.

$\begin{array}{ccccc}\hline \text { Student Test Grade } & \text { Quiz } 1 & \text { Quiz } 2 & \text { Quiz } 3 \\\hline 1 & 75 & 8 & 9 & 5 \\2 & 89 & 10 & 7 & 6 \\3 & 73 & 9 & 8 & 7 \\4 & 91 & 8 & 7 & 10 \\5 & 64 & 9 & 6 & 6 \\6 & 78 & 8 & 7 & 6 \\7 & 83 & 10 & 8 & 7 \\8 & 71 & 9 & 4 & 6 \\\hline\end{array}$
The professor fit a first-order model to the data that he intends to use to predict a student's grade on the first test using that student's grades on the first three quizzes.

Test the null hypothesis $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 0$ against the alternative hypothesis $H _ { \mathrm { a } }$ : at least one $\beta _ { i } \neq 0$ . Use $\alpha = .05$ . Interpret the result.