The formula to calculate sample size is Z * √((P(1-P)/n)
Z is the Z-score for the confidence level, in this problem the confidence level is given as 95%, so Z = 1.96
P is the population, which is unknown, but we want it to be the largest value possible, so in the equation above, P is 0.5.
n is the sample size.
Now we have: 1.96* √((0.5 * 0.5)/n)
They want this sample size to be less than 0.04
So now we have:
1.96* √((0.5 * 0.5)/n) < 0.04
Multiply both sides by 1/1.96:
√((0.5 * 0.5)/n) < 0.04 *1/1.96
Simplify:
0.5 / √n < 4/196
Take the reciprocal of both sides:
√n / 0.5 < 196/4
Simplify:
√n/0.5 < 49
Multiply both sides by 0.5:
√n = 49*0.5
√n = 24.5
to solve for n, raise both sides to the power of 2:
n = 24.5^2
n = 600.25
The sample needs to be about 600 people.
