Final answer:
A 90% confidence interval for the population mean indicates that if many samples were taken and the interval computed for each, approximately 90% of those intervals would contain the true population mean.
Step-by-step explanation:
When constructing a 90% confidence interval for the true population mean, it is essential to understand what is implied by this level of confidence. To say that we are 90 percent confident means that if we were to take a large number of random samples and compute a 90% confidence interval from each of these samples, then approximately 90 percent of these intervals are expected to contain the true population mean. This concept is a fundamental aspect of inferential statistics and measures how sure we are that the interval calculated from our sample statistics includes the parameter being estimated (the population mean in this case).
It is important to note that the 90% confidence level does not imply that the interval contains the sample mean with 90 percent probability. Instead, it refers to the long-term success rate of the process used to construct the confidence interval. As we construct more and more confidence intervals using the same method from different samples, the proportion of those intervals that contain the true population mean is expected to be about 90 percent.