Answer and Step-by-step explanation:
To determine the required sample size for conducting a follow-up study with a confidence level of 95% and a margin of error of ±0.04, we need to use the formula for sample size calculation in estimating a population proportion.
The formula is:
\[ n = \frac{{z^2 \cdot p \cdot (1-p)}}{{E^2}} \]
Where:
- \( n \) represents the required sample size
- \( z \) is the z-score corresponding to the desired confidence level (95% corresponds to a z-score of approximately 1.96)
- \( p \) is the estimated population proportion (we will assume a value of 0.5 for maximum sample size to be conservative)
- \( E \) is the desired margin of error (±0.04)
Substituting the values into the formula, we have:
\[ n = \frac{{1.96^2 \cdot 0.5 \cdot (1-0.5)}}{{0.04^2}} \]
Simplifying the equation:
\[ n = \frac{{3.8416 \cdot 0.25}}{{0.0016}} \]
\[ n = \frac{{0.9604}}{{0.0016}} \]
\[ n = 600.25 \]
Rounding up to the nearest whole number, the required sample size is 601.
Therefore, a sample size of 601 would be needed to conduct a follow-up study that provides 95% confidence that the point estimate is correct to within ±0.04 of the population proportion.