Question

Gina surveys 28 of her friends to find out how many read more than 2 books last month. She finds that 19 of thrn read more than 2 books last month. Use "plus four" method to find the 95% confidence interval for the true percentage of Gina's friends who read more than 2 books last month.

Answer 1

since in plus four method we add 2 in sample success and 4 in sample size

sample success x =19+2 =		21
sample size          n=28+4 =		32
sample proportion p̂ =x/n=21/32 =		0.6563
std error se= √(p*(1-p)/n) =sqrt(0.6563*(1-0.6563)/32)=		0.0840
for 95 % CI value of z=		1.960
margin of error E=z*std error   =1.96*0.0840=		0.1646
lower bound=p̂ -E                       =0.6563-0.1646=		0.4917
Upper bound=p̂ +E                     =0.6563+0.1646=		0.8209
from above 95% confidence interval for population proportion =(0.4917 , 0.8209)