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)

Question

asked Nov 15, 2020 160k views

1 Answer

Dimir · Answer 1 · 2020-11-20T06:37:56+0000

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

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