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 ŷ = 9.6 + 0.77x. The standard error of b₁ 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 =

(b) Would you reject this null hypothesis versus the one-sided alternative that the slope is positive? Explain your answer.
P =  

Answer 1

Sample size = n = 82

The regression equation is  ŷ = 9.6 + 0.77x.

b1 = 0.77

Sb1 = Standard error = 0.42

a)

The null and alternative hypothesis is

H0: $\beta$ = 0

H1: $\beta \neq$ 0

Level of significance = 0.05

Test statistic is

b1 0.77 Sb1 0.42 1.833

df = n - 2 = 82 - 2 = 80

P-value = 2*P( T > 1.833) = 0.0705

t =	1.833
df =	80
P =	0.0701

b)

The null and alternative hypothesis is

H0: $\beta$ = 0

H1: > 0

P-value = P(T > 1.833) = 0.0352

P = 0.0352

P-value < 0.05 we reject null hypothesis.

Conclusion: The slope is positive.