A sample of 20 Trinity students is taken, four of whom (4/20 = 20%) say they study at least 35 hours per week during the academic year. At most state universities, the proportion of students who report studying at least 35 hours a week is 10%. We wish to see if the Trinity sample provides strong evidence that the true proportion of Trinity students who study more than 35 hours a week is more than 10%.

Two different approaches were taken in order to yield a p-value.

Option #1: 1000 sets of 20 "coin tosses" were generated where the probability of heads was 10%. Out of the 1000 sets of tosses, 129 sets had at least 4 head occur, and so a p-value of 0.129 is obtained, showing no evidence that more than 10% of Trinity students study more than 35 hours per week.

Option #2: The test of significance calculator (theory-based approach) was used, generating a z-score of 1.49 with a p-value of 0.068, yielding moderate evidence that more than 10% of Trinity students study more than 35 hours a week.

Briefly explain which p-value (Option #1 or Option #2) is more valid and why.