Can a pretest on mathematics skills predict success in a statistics course? The

Question

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 = 9.2 + 0.77x. The standard error of b_1 was 0.42. (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. (Round your test statistic to three decimal places and your P-value to four decimal places.) Conclusion We reject H_0 at the 5% significance level. We do not reject H_0 at the 5% significance level. (b) Would you reject this null hypothesis versus the one-sided alternative that the slope is positive? Explain your answer. Conclusion We could reject H_0 at the 5% significance level. We could not reject H_0 at the 5% significance level.

Explanation / Answer

a) t = 0.77 / 0.42 = 1.833

df = n - 2 = 82 - 2 = 80

For a two tailed test with 80 degrees of freedom and t = 1.833,

P = 2*P(t > 1.833) = 2*0.03526 = 0.0705

We do not reject Ho at 5% significance level.

b) For a one tailed test,

P = P(t > 1.833) = 0.0353

We reject Ho at the 5% significance level.

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