Question

Jazlyn decided to poll town residents about making the old mill a historical site.

To obtain a confidence level of 95% (z*-score of 1.96) and an estimated margin of error of 8%, what is the approximate minimum number of randomly chosen town residents she needs to survey?

n=p(1=-p).(Z^*/E)^2

A.6 residents
B.12 residents
C.150 residents
D.600 residents

Answer 1

The correct option is C.

Explanation:

From the given information it is clear that

`z^*=1.96`

`E=(8)/(100)=0.08`

The total possibilities are 2, either agree to making the old mill a historical site or disagree. The probability that the town residents will agree, is

`p=(1)/(2)`

It is given that

`n=p(1-p)* ((z^*)/(E))^2`

`n=(1)/(2)(1-(1)/(2))* ((1.96)/(0.08))^2`

`n=(1)/(4)* (24.5)^2`

`n=150.0625`

`n\approx 150`

The minimum number of randomly chosen town residents she needs to survey is 150. Therefore option C is correct.

Answer 2

The answer is C.150 residents