Question

Does a math pretest predict success? Can a pretest on mathematics skills predict success in a statistics course? The 62 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^=13.8+0.81x. The standard error of b1 was 0.43. (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. (b) Would you reject this null hypothesis versus the one-sided alternative that the slope is positive? Explain your answer.

Answer 1

a) we have to test

Ho: 1 = 0 Vs H1 : 1 0

Test statistic t = b1 / s.E(b1)

t = 0.81/0.43

t = 1.88

tCritical for a = 0.05 and d.f = n -2 = 62 -2 = 60

tCritical = t​​​​​​a/2 , d.f = t​​​​​​0.025, 60

tCritical = 2.00

Decision rule : if t > 2.00 we reject the null hypothesis otherwise we fail to reject the null hypothesis

Our t = 1.88 < 2.00

Decision : we fail to reject the null hypothesis

Conclusion : There is no sufficient evidence to support the linear relationship between the pretest score and the score on the final exam

b) if alternative hypothesis is one tailed ( right tailed)

H1 : 1 > 0

tCritical for right tailed test

tCritical = t​​​​​​1-a , n-2​​​​ = t​​​​​​0.95, 60

tCritical = 1.67

So t = 1.88 > 1.67

Decision : we reject the null hypothesis

Conclusion : There is sufficient evidence to support the claim that there is positive linear relationship.