Question

A random sample of 133 people was taken from a very large population. Sixty-five of the people in the sample were females.The standard error of the proportion of females is (Round your answer to 4 decimal places.)

Answer 1

Answer: 0.0433

Step-by-step explanation:

Given: Sample size : n= 133

The number of females in sample = 65

Then the proportion of females : $P=\dfrac{65}{133}$

The formula to calculate the standard error of the proportion is given by :-

$S.E.=\sqrt{\dfrac{P(1-P)}{n}}$

$\Rightarrow S.E.=\sqrt{\dfrac{\dfrac{65}{133}(1-\dfrac{65}{133})}{133}}\\\\\Rightarrow\ \Rightarrow S.E.=0.0433444676341\approx0.0433$

Hence, the standard error of the proportion of females is 0.0433.