Question

Assume that the population proportion is 0.46. Compute the standard error of the proportion, σp, 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.)

Answer 1

Answer with explanation:

Given: The population proportion: p = 0.46

Standard error =
`\sigma_p=\sqrt{(p(1-p))/(n)}` , where n= sample size.

a) n= 500,000

`\sigma_p=\sqrt{(0.46(1-0.46))/(500000)}`

`=\sqrt{(0.46* 0.54)/(500000)}=√(0.0000004968)\approx0.00070`

b) n= 1,000,000

`\sigma_p=\sqrt{(0.46(1-0.46))/(1000000)}`

`=\sqrt{(0.46* 0.54)/(1000000)}=√(0.0000002484)\approx0.00050`

c) n= 5,000,000

`\sigma_p=\sqrt{(0.46(1-0.46))/(5000000)}`

`=\sqrt{(0.46* 0.54)/(5000000)}=√(0.00000004968)\approx0.00022`

d) n= 10,000,000

`\sigma_p=\sqrt{(0.46(1-0.46))/(10000000)}`

`=\sqrt{(0.46* 0.54)/(10000000)}=√(0.00000002484)\approx0.00016`

e) n= 100,000,000

`\sigma_p=\sqrt{(0.46(1-0.46))/(100000000)}=√(0.000000002484)\approx0.00004`

`=\sqrt{(0.46* 0.54)/(500000)}=√(0.0000004968)\approx0.00070`