Question

The population proportion is 0.5. What is the probability that a sample proportion will be within +/- 0.05 of the population proportion for each of the following sample sizes? Round your answers to 4 decimal places. Use z-table.

a.	n=100
b.	n=200
c.	n=500
d.	n=1,000

Answer 1

a)

here population proportion=     μp=	0.5000
sample size       =n=	100
std error of proportion=σp=√(p*(1-p)/n)=	0.0500

probability =P(0.45<X<0.55)=P((0.45-0.5)/0.05)<Z<(0.55-0.5)/0.05)=P(-1<Z<1)=0.8413-0.1587=0.6826

b)

std error of proportion=σp=√(p*(1-p)/n)=

0.0354

probability =P(0.45<X<0.55)=P((0.45-0.5)/0.035)<Z<(0.55-0.5)/0.035)=P(-1.41<Z<1.41)=0.9207-0.0793=0.8414

c)

std error of proportion=σp=√(p*(1-p)/n)=

0.0224

probability =P(0.45<X<0.55)=P((0.45-0.5)/0.022)<Z<(0.55-0.5)/0.022)=P(-2.23<Z<2.23)=0.9871-0.0129=0.9742

d)

std error of proportion=σp=√(p*(1-p)/n)=

0.0158

probability =P(0.45<X<0.55)=P((0.45-0.5)/0.016)<Z<(0.55-0.5)/0.016)=P(-3.16<Z<3.16)=0.9992-0.0008=0.9984