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-square regression line for predicting the score y on the final exam from the pretest score x was y^ = 15.3 + .72x (note: y caret). The standard error of B1 was 0.38.
We wish to 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.
a. State the statistical hypotheses.
b. Assuming all assumptions are valid, compute the test statistic.
c. What are the degrees of freedom for this test?
d. What is the p-value?
e. Do you reject or fail to reject the null hypothesis?
f. Write a proper conclusion.