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 = 9.5 + 0.75x. 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.) t = df = P = 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. P = Conclusion We could reject H_0 at the 5% significance level. We could not reject H_0 at the 5% significance level.

Explanation / Answer

Ans:

Test statistic:

t=b1/sb1

t=0.75/0.42=1.786

degree of freedom=n-2=82-2=80

a)p-value(two tailed)=0.0779

As,p-value>0.05,we fail to reject null hypothesis H0.

We do not reject H0 at 5% significance level.

b)p-value(right tailed)=0.0389

As,p-value<0.05,we reject H0.

We could reject H0 at the 5% significance level.

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