A political party is interested in finding out what kind of popular support they might expect on an environmental initiative.Similar issues have gotten 87% support.The committee will set up a polling program to assure 95% confidence that the margin of error is less than 9%.What sample size will suffice?

Question

Quizplus · Accepted Answer

We need to use the formula for sample size calculation for proportions:

n = (z^2 * p * q) / E^2

where:
z = z-score for the level of confidence (95% = 1.96)
p = estimated proportion (87% = 0.87)
q = 1 - p
E = maximum margin of error (9% = 0.09)

Plugging in the values:

n = (1.96^2 * 0.87 * 0.13) / 0.09^2
n = 53.64
n ≈ 54 (rounded up)

Therefore, the best choice is C with a sample size of 54.

A Political Party Is Interested in Finding Out What Kind