Question

28. test A population proportion is .40. A random sample of size 200 will be taken and the sa proportion p will be used to estimate the population proportion. a. What is the probability that the sample proportion will be within +.03 of the popu tion proportion? b. What is the probability that the sample proportion will be within +.05 of the popula- tion proportion? Aceume that the population proportion is .55. Compute the standard error of the proportion. 10

Answer 1

28)\

a)

for normal distribution z score =(phat-p)/$\sigma$p
here population proportion=     p=	0.400
sample size       =n=	200
std error of proportion=$\sigma$p=$\sqrt{}$(p*(1-p)/n)=	0.0346

hence probability that sample proportion will be within -/+ 0.03 of population proportion:

probability =

P(0.37<X<0.43)

=

P(-0.87<Z<0.87)=

0.8078-0.1922=

0.6156

b)

probability that sample proportion will be within -/+ 0.05 of population proportion:

probability =

P(0.35<X<0.45)

=

P(-1.44<Z<1.44)=

0.9251-0.0749=

0.8502