Hi, I have a question about hypothesis testing. I understand that if the value of a test statistic is within the critical region you reject null hypothesis. Is it correct to say that the p-value is the probability of obtaining that value? If the probability value is 30%, is it correct to say that there is a 30% chance of obtaining that value, and you would most likely be accepting null hypothesis? Finally, the critical region for a t14,0.025 = +/- 2.1448 and t14,0.05 = +/-1.7613, so if the test statistic value was 2, you would accept null hypothesis at 2.5%, but reject at 5% level...What is the significance of this?? Would appreciate any comments... Thanks Nik
Apologies if you sat this on Thursday last week and my reply is too late. The p-value is equal to the P(type 1 error) = prob of rejecting the null hypothesis when it's true. So if the p-value is 30% then if you reject the null hypothesis there's a 30% chance that you've bodged it. Which is bad. Hence we only reject the null hypothesis if the p-value is less than 5%. So there's a 95% chance we didn't reject it when it's correct. I'm assuming that it is a one-sided test (otherwise the p-value is double these probabilities) in which case you would say the p-value is between 2.5% and 5%. This means we can reject the null hypothesis at 5% but we can't quite reject it at the 2.5% value. (It would be unusually to test it at the 2.5% level - however you would be correct in saying we wouldn't reject it at the 2.5% level).
