Question

Suppose a simple random sample of 26 male students is asked whether they have pulled an "all-nighter " for academic reasons and 10 answered "yes." Suppose a simple random sample of 25 female students is asked whether they have pulled an "all-nighter" for academic reasons and 8 answered "yes."

Find the test statistic?

Answer 1

	Male		Female
x1                =	10	x2                =	8
p̂1=x1/n1 =	10/26=0.3846	p̂2=x2/n2 =	8/25=0.3200
n1                       =	26	n2                       =	25
estimated prop. diff =p̂1-p̂2    =0.3846-0.32=		0.0646
pooled prop p̂ =(x1+x2)/(n1+n2)=(10+8)/(26+25)=		0.3529
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =sqrt(0.3529*(1-0.3529)*(1/26+1/25))=		0.1339
test stat z=(p̂1-p̂2)/Se =		0.4826 ~ 0.48 (2 decimals)