Question

Assume that the population proportion is 0.42. Compute the standard error of the proportion,

σ_p,

for sample sizes of 500,000; 1,000,000; 5,000,000; 10,000,000; and 100,000,000. (Round your answers to five decimal places.)

sample size of 500,000sample size of 1,000,000sample size of 5,000,000sample size of 10,000,000sample size of 100,000,000

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

The standard error of the sample proportion,

σ_p,

  ---Select--- increases decreases and becomes extremely  ---Select--- small large as the sample size becomes huge.

Answer 1

Solution

Given that,

p = 0.42

1 - p = 1-0.42 = 0.58

1) n = 500000

= p = 0.42

=  [p ( 1 - p ) / n] =   [0.42*(0.58) /500000 ] = 0.00070

2)

n = 1000000

= p = 0.42

=  [p ( 1 - p ) / n] =   [0.42*(0.58) /1000000 ] = 0.00049

3)

n = 5000000

= p = 0.42

=  [p ( 1 - p ) / n] =   [0.42*(0.58) /5000000 ] = 0.00022

4)

n =10000000

= p = 0.42

=  [p ( 1 - p ) / n] =   [0.42*(0.58) /10000000 ] = 0.00016

and

5)

n =100000000

= p = 0.42

=  [p ( 1 - p ) / n] =   [0.42*(0.58) /100000000 ] = 0.00005

the standard error of the sample proportion as the sample size is increased,

σ_p, decreases .