Final answer:
The superintendent should use a simple random sample to estimate the percent of district residents supporting the building of a new middle school, ensuring equal selection chances for all residents, and may apply inferential statistics to interpret the sample data.
Step-by-step explanation:
The most appropriate method for the superintendent of a large school district to estimate the percent of district residents who support the building of a new middle school would be to conduct a simple random sample. This type of sampling ensures that every resident of the district has an equal chance of being selected. To obtain a more accurate estimate, the superintendent could use a sampling frame that includes all households or residents within the district and then randomly select a sufficient number of participants to ensure the sample is representative of the population.
For example, if the district has a large number of residents, the superintendent might decide to sample several hundred or even a few thousand residents. Drawing from the principles of inferential statistics, methods like the normal approximation to the binomial distribution can be applied to calculate various probabilities or construct confidence intervals for the true proportion of supporters, based on the sample data collected.