Final answer:
The true statement is that if we were to repeat the polling process many times, 95% of the 95% confidence intervals constructed would contain the true population proportion. This aligns with the definition of confidence intervals.
Step-by-step explanation:
The main answer to the student's question is true. If we were to repeat a polling process many times, each time calculating a 95% confidence interval for the proportion of interest, we would expect that 95% of these confidence intervals would indeed contain the true population proportion. This is by definition of a confidence interval. For example, when a poll suggests that 79% of California adults believe that education and schools are one of the top issues, and we construct a 90% confidence interval for this proportion, we are saying we are 90% confident that the true proportion falls within our calculated interval. If we were to collect many samples and construct intervals in this way, we would expect 90% of them to contain the true proportion.In conclusion, by constructing confidence intervals, we gain an estimated range that is likely to contain the true parameter of interest with a certain level of confidence, provided that the samples are random and the methodology is correct.