A midterm exam in Applied Mathematics consists of problems in 8 topical areas. One of the teachers believes that the most important of these is the section on problem solving. She analyzes the scores of 36 randomly chosen students using computer software and produces the following print-out relating the total score to the problemsolving subscore, ProbSolv: Predictor Coeff StDev T P
Constant 12.960 6.228 2.08 0.045
ProbSolv 4.0162 0.5393 7.45 0.000
S = 11.09 R-Sq = 62.0% R-Sq(adj) = 60.9%
(a) What is the predicted Total Score is the ProbSolve scores was 20?
(b) What is the residual for the data point (10, 55)?
(c) Calculate the 95% confidence interval of the slope of the regression line for all Applied Mathematics students.
(d) Use the information provided to test whether there is a significant relationship between the problem solving subsection and the total score at the 5% level.
(e) Are the decisions reached through the construction of the confidence interval and through the use of a significance test consistent. Explain.