Free Regression slope intervals Practice Problems • Learn To Be

Desiree is interested in the relationship between caffeine consumption and hours spent studying at her university. She randomly selects

20

students at her school and records their caffeine intake (mg) and the amount of time spent studying in a given week.

A computer output from a least-squares regression analysis on these data is shown below.

Predictor	Coef	SE Coef	T	P
Constant	$2.544$	$0.134$	$18.955$	$0.000$
Hours Studying	$0.164$	$0.057$	$2.862$	$0.005$

S=1.532\quad R\text{-}Sq=60.032\%\quad R\text{-}Sq (adj) = 58.621\%

If Desiree's $95\%$ confidence interval for her regression slope is $\left(0.044, 0.284\right)$ , which of the following is a true statement?

Choose 1 answer:

A
$95\%$ of the $20$ students sampled spend between $0.044$ and $0.284$ hours studying per week.
B
There is a $0.95$ probability that for the $20$ selected students, the predicted change in caffeine consumption for each additional hour of studying is between $0.044$ and $0.284$ mg.
C
There is a $0.95$ probability that the true mean change in hours of studying for each additional mg of caffeine consumed is is between $0.044$ and $0.284$ mg.
D
If $95\%$ confidence intervals are calculated from all possible samples of $20$ students, the true mean change in hours of studying for each additional mg of caffeine consumed will be contained in $95\%$ of these intervals.
E
If $20$ random samples of students were taken, $19$ of the resulting confidence intervals would capture the true mean hours of studying for each additional mg of caffeine consumed.

Regression slope intervals