Run the simulation code in the initial part of the education and salary question.

(a) Generate \(t\) statistics for the coefficient on education for each simulation. What are the minimal and maximal values of these \(t\) statistics?

(b) Generate two-sided \(\mathrm{p}\) values for the coefficient on education for each simulation. What are the minimal and maximal values of these \(\mathrm{p}\) values?

(c) In what percent of the simulations do we reject the null hypothesis that \(\beta_{\text {Education }}=0\) at the \(\alpha=0.05\) level with a two-sided alternative hypothesis?

(d) Re-run the simulations, but set the true value of \(\beta_{\text {Education }}\) to zero. Do this for 500 simulations, and report what percent of time we reject the null at the \(\alpha=0.05\) level with a two-sided alternative hypothesis.