Question

The population proportion is .80. What is the probability that a sample proportion will be within +/- .03 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=1000

Answer 1

It is known that,

for large sample sizes (n > 30),

a) If n = 100,

or

Now,

b) If n = 200,

or

Now,

P( 0.8 003)-0.80.03 Plp-0.8| < 0.03) P( 4 0.02828430.0282843 ) = P(|Z| < 1.06066) - , ,

Plp-0.8] < 0.03) 0.855578-0.144422

c) If n = 500,

or

Now,

d) If n = 1000,

or

Now,

Plp-0.8] < 0.03) 0.99 1147-0.0088530