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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?

Lui H
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  • You does not seem to give *any* definition, so if you are asked to give a precise one, then it sounds like you missed the point... – Tim May 28 '18 at 20:32
  • Thanks. Would a better attempt be : "We have more extreme results than the given null hypothesis" – Lui H May 28 '18 at 20:38
  • You probably should start with reading some of the answers for the other questions tagged as [tag:p-value] (starting from the most up-voted ones) and then try giving the *definition* by yourself. – Tim May 28 '18 at 20:41
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    I don't understand how you can be given that Ho and Ha. It seems like a false dichotomy to me... But in any case, when using the binom.test function, the probability you would use is the probability for the null hypothesis. – Sal Mangiafico May 28 '18 at 20:53

1 Answers1

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I don't think that you have attempted to provide a "definition". To define something is to specify the nature and meaning of it. Try answering this question: What is a p-value? (Note that it is not essential to calculate a p-value in order to define it.)

See here: What is the meaning of p values and t values in statistical tests?

Michael Lew
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