Question

A survey finds that 55 people out of 170 favor increasing property taxes to help pay for a new library. If this data is used to estimate the population proportion who favor new taxes, the standard error of the estimate is:

A. 0.425

B. 0.036

C. 0.324

D. 0.001

E. 0.119

Answer 1

Answer: B. 0.036

Explanation:

Formula for standard error :

`SE=\sqrt{(p(1-p))/(n)}`

, where p = Population proportion and n= sample size.

Let p be the population proportion of the people who favor new taxes.

As per given , we have

n= 170

`p=(55)/(170)\approx0.324`

Substitute these values in the formula, we get

`SE=\sqrt{(0.324(1-0.324))/(170)}\\\\=√(0.00129)\\\\=0.0359165699921\approx0.036`

Hence, the standard error of the estimate is 0.036.

∴ The correct answer is OPTION B. 0.036