The conservative sample size required for a 95 percent confidence interval for π with an error of ± 0.04 is
A)271
B)423
C)385
D)601

Question

Quizplus · Accepted Answer

The formula for the required sample size for a confidence interval for a proportion is given by:

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

where 
z = z-score for the desired confidence level (1.96 for 95% confidence level) 
p = estimated proportion of successes 
q = 1 - p 
E = margin of error

For a conservative estimate, we use the worst-case scenario where p = 0.5 (since this provides the largest possible value of n for any given E).

Plugging in the values, we get: 
n = (1.96^2 * 0.5 * 0.5) / 0.04^2 
n = 600.25

Rounding up to the nearest integer, the required sample size is 601. Therefore, the answer is D.

The Conservative Sample Size Required for a 95 Percent Confidence