Final answer:
A 95% confidence interval for the sample mean indicates that 95% of such intervals from repeated sampling would likely contain the true population mean. The interval is derived from sample data and reflects the range the true mean is believed to be within, with a 5% chance the mean lies outside it.
Step-by-step explanation:
A 95% confidence interval for the sample mean is a range in which we are 95% confident that the true population mean lies. The interpretation of this interval is based on the idea that if we were to take multiple samples and compute a confidence interval from each sample, 95% of those intervals would contain the true population mean. If the interval is (1.8, 2.2), this implies that either the true mean μ is within this range, or our sample mean is not within 0.2 units of the true mean μ, and the latter scenario would only happen in 5% of all possible samples. Notably, a 99% confidence interval would be wider than a 95% confidence interval because it encompasses more of the data distribution, aiming to include the true mean 99% of the time, at the cost of width.