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.

Step-by-step explanation:

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

$n=p(1-p)(\frac{z^*}{E})^2$, 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: $n=(\frac{1.96}{0.02})^2(0.61)(1-0.61)$

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

Hence, we need to survey 2285 Americans.