Answer :
Final answer:
To determine the needed sample size with 80% confidence within 2%, you can use a calculation formula with the Z-score and values for proportion and margin of error, yielding a result of approximately 169.
Explanation:
To calculate the sample size needed with 80% confidence within 2%, you can use the formula:
n = (Z^2 * p * (1-p)) / E^2
Where:
- n = required sample size
- Z = z-score for the desired confidence level (1.28 for 80% confidence)
- p = estimated proportion (145/500 in this case)
- E = margin of error (0.02)
Plugging in the values, the calculation yields:
n = (1.28^2 * 0.29 * 0.71) / 0.02^2 ≈ 169
Therefore, the sample size needed is 169.
