Question

Assume that the population proportion is .55. Compute the standard error of the proportion, ( ), for sample sizes of 100, 200, 500, and 1000 (to 4 decimals)

Answer 1

Answer with explanation:

The formula to find the standard error :-

$S.E.=\sqrt{\dfrac{P\cdot Q}{n}}$, where n is the sample size , P is the population proportion and Q=1-P .

Given : The population proportion $: P=0.55$

Then, $Q=1-0.55=0.45$

For n=100

$S.E.=\sqrt{\dfrac{(0.55)\cdot (0.45)}{100}}\\\\\Rightarrow\ S.E.\approx0.0497$

For n=200

$S.E.=\sqrt{\dfrac{(0.55)\cdot (0.45)}{200}}\\\\\Rightarrow\ S.E.\approx0.0352$

For n=500

$S.E.=\sqrt{\dfrac{(0.55)\cdot (0.45)}{500}}\\\\\Rightarrow\ S.E.\approx0.0222$

For n=1000

$S.E.=\sqrt{\dfrac{(0.55)\cdot (0.45)}{1000}}\\\\\Rightarrow\ S.E.\approx0.0157$