Let X ∼ B i n o m i a l ( n , p...

Lorena Beard

Lorena Beard

Answered

2022-07-10

Let X B i n o m i a l ( n , p )
H + 0 : p .5
H 1 : p < .5
How do we evaluate the p-value?
ie. P ( X x p >= .5 )
I have seen settings where this is just interpreted as P ( X x p = .5 ), but I'm not sure how this is the same thing.

Answer & Explanation

Marisol Morton

Marisol Morton

Expert

2022-07-11Added 13 answers

your system of Hypothesis is equivalent to the following
{ H 0 : p = 1 2 , H 1 : p < 1 2 ,
Thus the p-value is calculated as follows:
P [ X k | p = 1 2 ]
Example: to test the Hypothesis System above stated, we use a random sample of size n = 15 observing k = 4 successes.
The p-value is 5.92 %.

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