Question

The General Social Survey reported a sample where about 61% of US residents thought marijuana should be made legal. If we wanted to limit the margin of error of a 95% con dence interval to 2%, about how many Americans would we need to survey?

Answer 1

Answer: we need to survey 2285 Americans.

Explanation:

When population proportion (p) is known, then the formula to evaluate the sample size( minimum) is given by :-

`n=p(1-p)((z^*)/(E))^2`, where E = margin of error , z* = critical z-value.

Given: p= 0.61, E=0.02, Critical z value for 95% = 1.96

Required sample size:
`n=((1.96)/(0.02))^2(0.61)(1-0.61)`

`=(98)^2(0.61)(0.39)\\\\=9604(0.61)(0.39)\\\\\approx$$2285`

Hence, we need to survey 2285 Americans.