Is it possible to evenacceptthe null hypothesis? In introductory stats course I was taught that that null is never accepted, but rather we fail to reject it (this was done for tests absed only on p-values.) However, in a Mathematical Statistics course I took (we used Introduction to Mathematical Statistics by Hogg, McKean, Craig) the text often talked about accepting the null. In online resources, I see differing opinions. I've read that the null is never accepted, and I've also read that it can be accepted if you "accrue" enough evidence in support of it, either through confidence intervals or power functions - source: http://w3.sista.arizona.edu/~cohen/P...ohenIEEE96.pdf