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 = 9.3 + 0.79x. The standard error of b1 was 0.41.

(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.)

t =

df =

P =

Conclusion:

a. We reject H0 at the 5% significance level.

b. We do not reject H0 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.

P =

Conclusion

a. We could reject H0 at the 5% significance level.

b. We could not reject H0 at the 5% significance level.

Explanation / Answer

a) t = b1 / sb1 = 0.79 / 0.41 = 1.927

df = n - 2 = 82 - 2 = 80

P = 2*P(t > 1.927) = 2*0.0288 = 0.0576

Since p - value is greater than 0.05, conclusion will be:

b. We do not reject H0 at the 5% significance level.

b) For a one tailed test,

p - value = 0.0288

Since p - value is less than 0.05, the conlcusion will be:

a. We could reject H0 at the 5% significance level.

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