We are given the following experiment:
Consider an experiment which is a Bernoulli trial: it either succeeds with probability p or fails with probability 1− p; trials are independent of one another. Throughout this question we specify a null hypothesis H0 : p = 1/ 2 , and an alternative hypothesis HA : p = 2/ 3 . We perform the experiment 50 times, and our observation is r = 33 successes and 17 failures. Only one-sided tests are considered here.
We are asked to give a precise definition of the p-value. I don't understand what the question is asking really but I attempted it.
Attempt:
> dbinom(33,50,0.66)
[1] 0.1184165]
Our p-value is greater than 0.5 meaning we reject the null hypothesis.
Am I answering the question correctly or did I misunderstand the question entirely?