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{(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{((0.55)\cdot (0.45))/(100)}\\\\\Rightarrow\ S.E.\approx0.0497`

For n=200

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

For n=500

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

For n=1000

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