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Marty McMath Makes Predictions from Computer Output

APSTAT-1X42FU

Marty McMath wants to know if a student's final grade in Algebra II can be used to predict his or her final grade in Precalculus. To investigate, he gathers data from a random sample of $8$ students who have completed both courses.

After noticing that the relationship is roughly linear and confirming that the conditions have been satisfied, he decides to use statistical software to conduct a $2$-sided $t$-test for linear regression where the null hypothesis is the slope equals $0$.

Computer output is shown below.

Predictor Coef SE Coef T
Constant 16.46 3.73 4.41
Algebra II 0.82 0.22 3.73



Unfortunately, he can't figure out how to make the computer output display the $p$-value. Luckily, he knows enough statistics to be able to calculate it from the output shown.

What is the $p$-value?

A

$0.005$

B

$0.007$

C

$0.01$

D

$0.1$

E

$0.22$