The Regression Output Below Is the Result of Testing Whether

question 10

Multiple Choice

The regression output below is the result of testing whether there is an association between the number of hours of sleep a student had the night before an exam and the number of questions
Answered correctly on the exam. Assume that the conditions of the linear regression model are
Satisfied. What is the 95% confidence interval for the intercept (rounded to the nearest hundredth) ?
Does this interval support the theory that the intercept is zero? Choose the statement that
Summarizes your answer in context. $\begin{array}{|l|l|l|l|l|}\hline & \text { Coefficients } & \begin{array}{l}\text { Standard } \\\text { Error }\end{array} & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -0.25 & 1.85713484 & -4.64144652 & 4.14144652 \\\hline \text { Slope } & 0.087621024 & 0.023022636 & 0.033181139 & 0.142060908 \\\hline\end{array}$

• A) \(( - 4.64,4.14 )\). This interval supports the theory that the intercept could be zero. In this context this would mean that a student who had zero hours of sleep could reasonably expect to get a zero on the test.
• B) \(( - 4.64,4.14 )\). This interval does not support the theory that the intercept could be zero. In this context this would mean that for approximately every \(0.08\) hours of sleep, the student could expect to get approximately one test question correct.
• C) \(( 0.03,0.14 )\). This interval does not support the theory that the intercept could be zero. In this context the intercept is greater than zero so a student could expect to get a positive score on the test even if they did not get any hours of sleep.
• D) None of these

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