To estimate the proportion of single-person households out of 20,000 households, a sample (MAS) will be selected. Knowing that in the last census this proportion was 11% and that in no way can it exceed 15% currently; determine the sample size to have a precision of 1% and a confidence of 99%.

To determine the sample size for a proportion estimation problem, we can use the following formula: n = (z^2 * p * q) / (e^2) where: n is the sample size z is the z-score for the desired confidence level p is the estimated proportion of the population with the desired characteristic q is the estimated proportion of the population without the desired characteristic e is the desired precision of the estimate In this case, we want a precision of 1% and a confidence of 99%. The z-score for a 99% confidence level is 2.576. We also know that the estimated proportion of single-person households is between 11% and 15%. To be conservative, we will use the highest estimated proportion, which is 15%. Therefore, the sample size required is: n = (2.576^2 * 0.15 * 0.85) / (0.01^2) = 6497 Therefore, the sample size required to estimate the proportion of single-person households with a precision of 1% and a confidence of 99% is 6497. Note that this sample size is calculated assuming that the sample is drawn randomly from the population of 20,000 households. If the sample is not drawn randomly, then the sample size may need to be increased.