Final answer:
The correct interpretation of a 90% confidence interval is that if multiple samples are taken and confidence intervals are constructed, about 90% of those intervals will contain the true population mean. The width of the confidence interval increases with the confidence level, with a 95% interval being wider than a 90% interval.
Step-by-step explanation:
The correct interpretation of the statement regarding a 90% confidence interval for an unknown population mean μ (mu) is that if we were to take repeated samples and compute confidence intervals from those samples, about 90% of those intervals would contain μ. It's a common misconception to think that the probability that μ is in this interval is 90%, but the interval is either correct or not for the specific sample we have; the probability is about the process of creating intervals, not the interval itself.
To construct a confidence interval for a population mean with a known standard deviation, we use the sample mean (x) as an estimate for μ and account for the margin of error (EBM). The confidence interval has the form (point estimate - EBM, point estimate + EBM).
Comparing different confidence levels, a 95% confidence interval will naturally be wider than a 90% confidence interval. This is because a higher confidence level requires capturing a larger portion of the normal distribution's probability, thus widening the interval to be more certain it contains μ.