Final answer:
The true statement about 95% confidence intervals is that 'We are 95% confident that the true population mean is within the interval.' This is about the confidence in the process over many samples, not the probability within one specific interval.
Step-by-step explanation:
The correct response to the student's question about 95% confidence intervals is D. We are 95% confident that the true population mean is within the interval. This does not mean that the true population mean has a 95% chance of being within the interval on any single confidence interval calculated. Instead, if we were to take many samples and calculate a 95% confidence interval from each sample, we would expect about 95% of these intervals to contain the true population mean.
Thus, the statement 'We are 95% confident' relates to the process over many samples rather than the probability for one specific interval. The concept of a confidence interval is that, given a level of confidence (in this case, 95%), if we were to repeat our sampling and interval calculations multiple times, a stated percentage of those intervals would contain the true population mean. Therefore, the wider the confidence interval, the higher the probability that it will contain the true mean, as indicated by a comparison between 90% and 95% confidence intervals, where the 95% interval is wider.