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 = 9.1 + 0.79x. The standard error of b₁ was 0.41.

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 H₀ at the 5% significance level. or

We do not reject H₀ 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.

Conclusion

We could reject H₀ at the 5% significance level. or

We could not reject H₀ at the 5% significance level.

Answer 1

Answer :

given data :-

sample size = 82

   n = 82

regression line equation = ŷ = 9.1 + 0.79x

standard error = 0.41

(a).

t = (slope)/standard error

= 0.79 / 0.41

t = 1.926

df = n - 1

= 82 - 1

df = 81

For a two tailed test alpha = 0.05,

the p-value is

p-value = 0.0576

hence, p-value > value

so,

We do not reject Ho at 5% significance level.

(b) For a one tailed test,

alpha = 0.05,

the p-value is

p-value = 0.0288

hence, p-value < value

so,

We reject Ho at the 5% significance level.