I've got the correct answer to this, but when checking against the answer there's something fundamental I don't think I'm understanding. 'The p-value of F=124.7 is much less than even 0.01, so H0 is rejected at the 1% level.' When I go to the tables at the 5% level for a one sided test, I'm looking at F_1,n-2 = F_1,4 and get a value of 7.709 which is much less than 124.7 and the 1% value of F_1,4 is 21.2. Why is the answer saying the p value of F124.7 is less than even 0.01, ie, 1% level when it's not? On a separate note, when doing these tests we're not asked at what level to do these at. Sometimes the answer uses the 5% level, sometimes it uses the 1% level, why is this? Is it just trying to show how strong the evidence is for rejection? Thanks!
The p-value is the probability of a more extreme value than your observed statistic (ie the probability of being more in the tail). Hence, the more extreme your value is, the smaller the p-value and hence it's less than 1%. Does that help? With levels, 5% is the standard you should go for. But if we can reject at a higher level (ie a smaller tail) like 2.5% or 1% sometimes we say that to declare that we can "super"-reject the null hypothesis, if you like. However for exams, 5% will get you the right answer unless they explicitly ask you to test at a different level.
