Question

A survey shows that 45% of the respondents pick option A. Given that 50 people replied, what is the standard error of the proportion

Answer 1

The answer would be 0.07%

Answer 2

Answer: 0.07

Step-by-step explanation:

Given: A survey shows that 45% of the respondents pick option

i.e. P =45%= 0.45

Q=1-P=1-0.45=0.55

The total number of people replied n = 50

Now, the standard error of the proportion is given by :-

$\text{S.E.}=\sqrt{\dfrac{PQ}{n}}\\\\\Rightarrow\text{S.E.}=\sqrt{\dfrac{0.45\times0.55}{50}}\\\\\Rightarrow\text{S.E.}=\sqrt{0.00495}\\\\\Rightarrow\text{S.E.}=0.0703562363974\approx0.07$