Suppose a company offers tutoring to students interested in improving their math SAT scores. From a random sample of 100 previous customers, they find that Score ˆ = 502.7 + 1.45 · Hours, where Score is the SAT math score and Hours is the number of hours the student was tutored. The R-squared and residual standard error for this model is 0.855 and 16.54, respectively.
(a) For every additional 10 h of tutoring, what is the corresponding change in the test score?
(b) If the standard deviation of the hours variable is 27.5, what is the standard deviation of the score variable?
(c) Find a 95% confidence interval for the true slope.
(d) Find a 95% confidence interval for the mean score for students who are tutored 50 h. Assume the mean number of hours tutored is 55 h.