Question

# Can a pretest on mathematics skills predict success in a statistics course? The 82 students in...

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 =

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: = 0

H1: 0

Level of significance = 0.05

Test statistic is

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: = 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.

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