X i ∼ B e r n ( p ), Y = ∑ i = 1 N X i and H 0 : p ≥ 0.5 vs H 1 : p &lt; 0.5 with α = 0.05.I have to find the p-value at n = 30 and y = 5.I'm not sure if this correct, but I figured the p-value was simply: P ( Y ≤ 5 ) = ∑ i = 1 5 ( 30 y ) ( 0.5 ) y ( 0.5 ) 30 − y which works out to be 0.00016.If this is correct, then why have I been given α?

Question

X    i    ∼  B  e  r  n  (  p  ),   Y  =      ∑          i      =      1        N        X    i   and       H    0    :  p  ≥  0.5 vs       H    1    :  p  &amp;lt;  0.5 with   α  =  0.05.I have to find the   p-value at   n  =  30 and   y  =  5.I&#039;m not sure if this correct, but I figured the   p-value was simply:  P  (  Y  ≤  5  )  =      ∑          i      =      1        5                  (              30      y                  )        (  0.5      )    y    (  0.5      )          30      −      y      which works out to be   0.00016.If this is correct, then why have I been given   α?

scipionhi · Accepted Answer

The   p-value you calculated is correct.   α  =  5  % is given to compare the   p-value you found with it.As       p          v      a      l      u      e        &amp;lt;  α you reject       H    0  .

X i </msub> ∼ B e r n ( p ) , Y =

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