Ap Stat, Standard deviation of p^

Question

A 2010 study of 240 randomly-selected residents of a subtropical resort city with 82,000 residents found that 5.4% of them had been exposed to the mosquito-borne virus that causes Dengue fever. Suppose the actual percentage of people in the city who have been exposed to the virus is 3%. Let p^= the proportion of residents who have been exposed in a random sample of 240.

The standard deviation of p^ is approximately...

The answer is .0110, how do you get it?

Thanks!

Answer 1

The formula is √[p-hat(1 - p-hat)/n]. P-hat in this case is 0.03, so 1 - p-hat = 0.97.

√[(0.03 • 0.97)/240] ≈ 0.011011.