Math pretest predicts success? Can a pretest on mathematics skills predict success in a statistics course? The 82 students in an introductory statistics class took a pretest at the beginning of the semester. The least-squares regression line for predicting the score y on the final exam from the pretest score x was y^ = 16.23 + 0.82x. The standard error of b1 was 0.38.
(a) Test the null hypothesis that there is no linear relationship between the pretest score and the score on the final exam against the two-sided alternative.
(b) Would you reject this null hypothesis versus the one-sided alternative that the slope is positive? Explain your answer.