P = 0.30 vs P > 0.30
Given : x = 53, n = 150 , = x /n = 0.3533 , p = 0.30 and q = 1- 0.30 = 0.7
Rejection region : Reject H0 if x ≥ 53
i) Significance level ( α ) = P( Reject H0 , when H0 is true )
P ( x ≥ 53 Given P = 0.30 )
= P( ≥ 0.3533 , P = 0.30 )
=P( z ≥ 1.42 )
= 1 - P( z ≤ 1.42 )
= 1 - 0.9222 --- ( from z score table )
α = 0.0778
ii ) Power = P( Reject H0, when H0 is false )
#P ( x ≥ 53 Given P = 0.40 )
= P( ≥ 0.3533 , P = 0.40 )
=P( z ≥ -1.17 )
= 1 - P( z ≤ -1.17 )
= 1 - 0.1210 --- ( from z score table )
Power at 0.40 = 0.8790
# P ( x ≥ 53 Given P = 0.50 )
= P( ≥ 0.3533 , P = 0.50 )
= P( z ≥ -3.59 )
= 1 - P( z ≤ -3.59 )
= 1 - 0.0002 --- ( from z score table )
Power at 0.50 = 0.9998
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