Difficult# 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?