Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p = 0.18. You would like to be 99% confident that your esimate is within 1.5% of the true population proportion. How large of a sample size is required?

Answer 1

435,307

Explanation:

Given that :

p = 0.18

Zcritical = 99%

Error (E) = 1.5% = 1.5/100 = 0.0015

Sample size (n) can be obtained using the relation :

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

q = 1 - p ; q = 1 - 0.18 = 0.82

Zcrit at 99% equals 2.576

n = (2.576 / 0.0015)^2 * (0.18 * 0.82)

n = (1717.3333)^2 * (0.1476)

n = 2949233.66328889 * 0.1476

n = 435306.888701440164

n = 435,307 samples