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 = $\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}$  , where n= sample size.

a) n= 500,000

$\sigma_p=\sqrt{\dfrac{0.46(1-0.46)}{500000}}$

$=\sqrt{\frac{0.46\times 0.54}{500000}}=\sqrt{0.0000004968}\approx0.00070$

b) n= 1,000,000

$\sigma_p=\sqrt{\dfrac{0.46(1-0.46)}{1000000}}$

$=\sqrt{\frac{0.46\times 0.54}{1000000}}=\sqrt{0.0000002484}\approx0.00050$

c) n= 5,000,000

$\sigma_p=\sqrt{\dfrac{0.46(1-0.46)}{5000000}}$

$=\sqrt{\frac{0.46\times 0.54}{5000000}}=\sqrt{0.00000004968}\approx0.00022$

d) n= 10,000,000

$\sigma_p=\sqrt{\dfrac{0.46(1-0.46)}{10000000}}$

$=\sqrt{\frac{0.46\times 0.54}{10000000}}=\sqrt{0.00000002484}\approx0.00016$

e) n= 100,000,000

$\sigma_p=\sqrt{\dfrac{0.46(1-0.46)}{100000000}}=\sqrt{0.000000002484}\approx0.00004$

$=\sqrt{\frac{0.46\times 0.54}{500000}}=\sqrt{0.0000004968}\approx0.00070$