Suppose you run a chi square GOF test on a categorical variable with 2 levels and you reject the null (p= p0). If phat > p0, can you conclude that the population proportion is not only not equal to the hypothesized value, but is actually greater?
My guess is that you can say this because if the true proportion was less than p0, the chi square statistic would be even larger (and hence more unlikely to occur if H0 was true). However, I can't recall having seen this interpretation, so I'm a little wary of it.
I know this is probably a simple question, but I could not find any mention of it from an internet search, so even pointing me to a good reference would be appreciated.