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 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 = |
(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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