Question

Determine the required sample size if you want to be 80% confident that the sample proportion is within 4% of the population proportion if no preliminary estimate of the true population is available.

(Write your answer as a whole number)
________

Answer 1

To determine the required sample size without a preliminary estimate, we can use the conservative approach by assuming that the population proportion (p) is 0.5. This maximizes the sample size, ensuring the desired level of confidence and margin of error. The formula for calculating the sample size (n) is:

n = (Z^2 * p * (1-p)) / E^2

where Z is the Z-score corresponding to the desired confidence level (80% in this case), p is the population proportion (0.5), and E is the desired margin of error (4% or 0.04).

For an 80% confidence level, the Z-score is approximately 1.28. Plugging the values into the formula, we get:

n ≈ 320.25

Since the sample size should be a whole number, we round up to ensure the desired level of confidence and margin of error:

n ≈ 321

Your answer: 321