Question

Assume that the population proportion is 0.59. Compute the standard error of the proportion,

σ_p,

for sample sizes of 100, 200, 500, and 1,000. (Round your answers to four decimal places.)

For a sample size of 100For a sample size of 200For a sample size of 500For a sample size of 1000

What can you say about the size of the standard error of the proportion as the sample size is increased?

σ_p

increases as n increases.

σ_p

decreases as n increases.    

σ_p

approaches p as n increases.

σ_p

approaches

p

as n increases.

Answer 1

solution

Given that,

p = 0.59

1 - p = 1 - 0.59 =0.41

n= 100

p = (( * (1 - )) / n)

= (((0.59* 0.41) / 100) = 0.0492

n= 200

p = (( * (1 - )) / n)

= (((0.59* 0.41) / 200) = 0.0348

n= 500

p = (( * (1 - )) / n)

= (((0.59* 0.41) / 500) = 0.0220

n= 1000

p = (( * (1 - )) / n)

= (((0.59* 0.41) / 1000) = 0.0156

answer -=

σ_p

decreases as n increases.