In the province of Jaén there are 50 thousand 523 homes, of which 24 thousand 882 are of the urban area. It is desired to know the status of the same, knowing that by studies previous p= 0.60 How many homes should be chosen in each area, using a level 95% confidence level, and a 6% error?

To determine the sample size required using the given parameters, we use the formula for a stratified sample:

1. Determine the total number of homes and the number in urban and rural areas:
Total homes: N = 50523
Urban homes: N_1 = 24882
Rural homes: N_2 = 50523 - 24882 = 25641

2. Proportion of the sample from each stratum (urban and rural):
Urban: W_1 = \frac{N_1}{N} = \frac{24882}{50523}
Rural: W_2 = \frac{N_2}{N} = \frac{25641}{50523}

3. Use the formula for the sample size with a given confidence level and margin of error, the formula for sample size n is:
n = \left( \frac{Z^2 \cdot p \cdot (1-p)}{E^2} \right)

where:
- Z is the Z-value for a 95% confidence level (1.96),
- p is the estimated proportion (0.60),
- E is the desired margin of error (0.06).

4. Calculate the sample size:
n = \left( \frac{1.96^2 \cdot 0.60 \cdot (1-0.60)}{0.06^2} \right)
n = \left( \frac{1.96^2 \cdot 0.60 \cdot 0.40}{0.0036} \right)
n \approx 256

5. Allocate the sample size proportionally among strata (rounded to the nearest whole number):
Urban: n_1 = W_1 \cdot n = \frac{24882}{50523} \cdot 256 \approx 126
Rural: n_2 = W_2 \cdot n = \frac{25641}{50523} \cdot 256 \approx 130

Answer: Total sample size is 256 , with 126 homes from the urban area and 130 homes from the rural area.