Let X ∼ B i n o m i a l ( n , p ) H + 0 : p ≥ .5 H 1 : p &lt; .5How do we evaluate the p-value?ie. P ( X ≥ x ∣ p &gt;= .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.

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Let   X  ∼  B  i  n  o  m  i  a  l  (  n  ,  p  )  H  +  0  :  p  ≥  .5      H    1    :  p  &amp;lt;  .5How do we evaluate the p-value?ie.   P  (  X  ≥  x  ∣  p  &amp;gt;=  .5  )I have seen settings where this is just interpreted as   P  (  X  ≥  x  ∣  p  =  .5  ), but I&#039;m not sure how this is the same thing.

Marisol Morton · Accepted Answer

your system of Hypothesis is equivalent to the following      {                                                  H            0                    :          p          =                      1            2                    ,                                                            H            1                    :          p          &amp;lt;                      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  %.

Let X ∼ B i n o m i a l ( n , p ) H + 0 :

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