The Data Below Are the Final Exam Scores of 10

question 1

Multiple Choice

The data below are the final exam scores of 10 randomly selected history students and the number of hoursthey slept the night before the exam. Find the equation of the regression line for the given data. What would bethe predicted score for a history student who slept 15 hours the previous night? Is this a reasonable question?Round your predicted score to the nearest whole number. Round the regression line values to the nearesthundredth. $\begin{array}{l|c|c|c|c|c|c|c|c|c|c|}\text { Hours, } \mathbf{x} & 3 & 5 & 2 & 8 & 2 & 4 & 4 & 5 & 6 & 3 \\\hline \text { Scores, } \mathrm{y} & 65 & 80 & 60 & 88 & 66 & 78 & 85 & 90 & 90 & 71\end{array}$

• A) \(\hat { y } = 5.04 \mathrm { x } + 56.11 ; 132\); No, it is not reasonable. 15 hours is well outside the scope of the model.
• B) \(\hat { y } = 5.04 \mathrm { x } + 56.11 ; 132\); Yes, it is reasonable,
• C) \(\hat { y } = - 5.04 x + 56.11 ; - 20\); No, it is not reasonable.
• D) \(\hat { y } = - 5.04 \mathrm { x } + 56.11 ; - 20\); Yes, it is reasonable.

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Definitions:

Random Assignment

A method used in experiments where participants are allocated to different groups randomly, ensuring that each group is similar at the start of the experiment.

Projective Tests

Psychological tests that use ambiguous or vague images or situations to elicit responses that can reveal hidden emotions and internal conflicts.

Personality Psychology

The scientific study of individual differences in patterns of thinking, feeling, and behaving.

Proving Causation

The process of demonstrating that one event directly results in the occurrence of another event.