A Statistics Professor Gave Three Quizzes Leading Up to the First

question 99

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. $$\begin{array} { c c c c c } \hline \text { Student } &\text { Test Grade } &\text { Quiz 1 } & \text { Quiz 2 } & \text { Quiz 3 } \\\hline 1 & 75 & 8 & 9 & 5 \\2 & 89 & 10 & 7 & 6 \\3 & 73 & 9 & 8 & 7 \\4 & 91 & 8 & 7 & 10 \\5 & 64 & 9 & 6 & 6 \\6 & 78 & 8 & 7 & 6 \\7 & 83 & 10 & 8 & 7 \\8 & 71 & 9 & 4 & 6 \\\hline\end{array}$$ 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 $H _ { \mathbf { a } }$ : at least one $\beta _ { i } \neq 0$ . Use $\alpha = , 05$ . Interpret the result. α = .05. Interpret the result. 12.4 Using the Model for Estimation and Prediction 1 Find and Interpret Prediction Interval

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Definitions:

Cerebellum

A region of the brain that plays a key role in motor control, coordination, precision, and accurate timing of movements, also involved in some cognitive functions.

Fetus

A developing mammal or human from the end of the embryonic period (in humans, approximately 8 weeks after conception) until birth.

Motor Development

The progression of muscular coordination and the ability of the body to move and manipulate objects, which occurs in stages from simple reflexes to complex movements.

Cephalocaudal

A pattern of growth and development where physical and motor skills develop from the head downwards through the body.