Again, we care about the standard error (the standard deviation of the sampling distribution of sample means) because it expresses the degree of uncertainty we have in our estimation. Due to this, it's not uncommon for statisticians to report the standard error along with their estimate.
What's more common, though, is for statisticians to report a range of numbers to describe their estimates; this is called interval estimation. In contrast, when we were just providing the sample mean as our estimate of the population mean, we were engaging in point estimation.
One common approach to interval estimation is to use confidence intervals. A confidence interval gives us a range over which a significant proportion of the sample means would fall when samples are repeatedly drawn from a population and their means are calculated. Concretely, a 95 percent confidence interval is the range that would contain 95 percent of the sample means if multiple samples were taken from the same...
