Question

The population proportion is 0.40. What is the probability that a sample proportion will be within ±0.04 of the population proportion for each of the following sample sizes? (Round your answers to 4 decimal places.)

(a)n = 100

(b) n = 200

(c) n = 500

(d) n = 1,000

(e) What is the advantage of a larger sample size?

Answer 1

the population proportion p = 0.40

standard error =

to find the probability that a sample proportion will be within ±0.04 of the population proportion, we will use Z distribution

a) standard error for n= 100 is

the probability that a sample proportion will be within ±0.04 of the population proportion=

b)

standard error for n= 200 is

the probability that a sample proportion will be within ±0.04 of the population proportion=

c)

standard error for n= 500 is

the probability that a sample proportion will be within ±0.04 of the population proportion=

d)

standard error for n= 1000 is

the probability that a sample proportion will be within ±0.04 of the population proportion=

e) as the sample size increases the standard error reduces.