Question

Determine sample sizes for the following survey situations: a. Resident population of 1 million; confidence level of 99 percent; confidence interval of ±2 percent b. Resident population of 45,000; confidence level of 95 percent; confidence interval of ±5 percent

quickly please

Answer 1

a) As we are not given any prior proportion value, we use p = 0.5 to get a conservative value of sample size here.

For 99% confidence level, we get from the standard normal tables:
P(-2.576 < Z < 2.576) = 0.99

Therefore the margin of error here is computed as:

Therefore the sample size now is computed here as:

Therefore 4148 is the required sample size here.

b) From standard normal tables, we have:
P( -1.96 < Z < 1.96) = 0.95

Therefore for a 0.05 margin of error, the sample size here is computed as:

Therefore 385 is the required sample size here.