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Can a pretest on mathematics skills predict success in a statistics course? The 55 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 = 10.5 + 0.82x . The product of 0.82 times x (the pre-test score) + 10.5 predicts the score on the final exam, y. The standard error of b was 0.38. 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.

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So since 0.0308 is less than the significance level of 0.05, we reject the null hypothesis that β=0 and so there is evidence to believe that the null hypothesis may be true (i.e. that there IS a linear relationship).

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