Question

To test Ho: p = 0.38 versus H1: p < 0.38, a simple random sample of n = 1122 individuals is obtained. The researcher decides to test this hypothesis atα = 0.10 level of significance.

Compute the power of the test if the true population proportion is 0.35.

Answer 1

null Hypothesis:               Ho:   p		=	0.380
alternate Hypothesis:    Ha: p		<	0.380

std error   se =√(p*(1-p)/n) = sqrt(0.38*0.62/1122) =

0.0145

0.1 level and left tailed test critical value Zα=-1.28
rejection reg:p̂ <=po+Zα*σpo or p̂ <0.38-1.28*0.0145 =		0.3615

for true p=0.35

standard error of pa=√(pa*(1-pa)/n)=

0.0142

Power=P( p̂ <0.3615|p=0.35)=P(Z<(0.3615)/0.0142)=P(Z<0.8)=0.7881