Step 1 :We are given that the estimated proportion P is 0.21, the desired margin of error E is 0.025, and the z-score Z corresponding to a 90% confidence level is 1.645.
Step 2 :We can use these values in the formula for sample size estimation for proportions, which is \(n = \frac{{Z^2 \cdot P \cdot (1-P)}}{{E^2}}\).
Step 3 :Substituting the given values into the formula, we get \(n = \frac{{(1.645)^2 \cdot 0.21 \cdot (1-0.21)}}{{(0.025)^2}}\).
Step 4 :Solving this expression, we find that the required sample size is 719.
Step 5 :\(\boxed{719}\) is the final answer.