Question

Test the hypothesis using the​ P-value approach. Be sure to verify the requirements of the test. Upper H0: p=0.4 versus Upper H 1: p> 0.4 n=100​; x=50​, alpha= 0.01 Is np 0 (1 - p 0) >or equals ​10?   Yes    No

What is the P value? Can you please list the steps of how to find the P value

Answer 1

Condition check for Normal Approximation to Binomial
n * P >= 10 = 100 * 0.5 = 50
n * (1 - P ) >= 10 = 100 * ( 1 - 0.5 ) = 50

Yes, both are > 10

P = X / n = 50/100 = 0.5

Test Statistic :-
Z = ( P - P0 ) / √ ((P0 * q0)/n))
Z = ( 0.5 - 0.4 ) / √(( 0.4 * 0.6) /100))
Z = 2.0412

Decision based on P value
P value = P ( Z > 2.0412 ) = 0.0206 ( From Z table )

Looking for the value Z = 2.0412 in standard normal table, we will get probability value 0.0206

Reject null hypothesis if P value < α = 0.01
Since P value = 0.0206 > 0.01, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0