Question

In an opinion poll, 25% of a random sample of 200 people said that they were strongly opposed to having a state lottery. The standard error of the sample proportion is approximately_________.

Answer 1

Answer: 0.031 .

Step-by-step explanation:

The standard error of the sample proportion is given by :-

$SE_p=\sqrt{\dfrac{p(1-p)}{n}}$

, where p= Sample proportion and n is the sample size.

As per given , we have

In an opinion poll, 25% of a random sample of 200 people said that they were strongly opposed to having a state lottery.

i.e. p= 0.25 and n= 200

Then , the  standard error of the sample proportion $=\sqrt{\dfrac{0.25(1-0.25)}{200}}$

$=\sqrt{\dfrac{0.25\times0.75}{200}}=\sqrt{0.0009375}\\\\=0.0306186217848\approx0.031$

Hence, the standard error of the sample proportion is approximately 0.031 .