What sample size is required from a very large population to estimate a population proportion within
0.05 with 95% confidence? Don't assume any particular value for p.
A. 271
B. 38
C. 385
D. 767
To determine the sample size required to estimate a population proportion with a certain level of confidence, we can use the formula:
n = (Z^2 * p * (1-p)) / E^2
where:
- n is the required sample size
- Z is the z-score corresponding to the desired level of confidence (95% confidence corresponds to a z-score of approximately 1.96)
- p is the estimated proportion of the population (since we don't have a specific value for p, we can use the worst-case scenario which is 0.5 for maximum variability)
- E is the desired level of precision or margin of error (in this case, it is 0.05)
Using this formula, we can calculate the required sample size:
n = (1.96^2 * 0.5 * (1-0.5)) / 0.05^2
n = (3.8416 * 0.5 * 0.5) / 0.0025
n = 0.9604 / 0.0025
n ≈ 384.16
Since the sample size needs to be a whole number, you would round up to the nearest whole number to ensure you have enough individuals in the sample. Therefore, the required sample size is 385.
So, the correct answer is C. 385.