Prediction Intervals: Videos & Practice Problems

A psychology professor is interested in predicting students' final exam scores based on the number of hours they spent in study groups. For a sample of $42$ students, the regression equation is used to predict the score for a student who spent 8 hours in study groups. The predicted score is $82$ points. The standard error of estimate is $s=5.2$, the mean number of hours is $\bar{x}=6.5$, and $S_{xx}=120$. Construct a $95\%$ prediction interval for the exam score of a student who spent $8$ hours in study groups.