Question

Find the appropriate p-value to test the null hypothesis, H0: p1 = p2, using a significance level of 0.05.
n1 = 100 n2=200

x1= 38 x2= 40

A) .1610

B) .7718

C) .0412

D) .2130

Answer 1

Ho: p1 = p2,

Ha: p1 p2,

1=x1/n1=0.38

2=X2/n2=0.2

p=(x1+x2)/(n1+n2)=(38+40)/(100+200)=0.26

q=1-p=0.74

#test statistics

Z=(1-2)/sqrt(p*q/n1+p*q/n2)

Z=(0.38-0.2)/sqrt(0.26*0.74/100+0.26*0.74/200)

Z=3.3506

P-value=P(|Z|>3.3506)=2*P(Z>3.3506)=2*0.0004=0.0008

#P-value=0.0008