In statistics, what term means "a numerical range around a sample mean accompanied with a statement of how confident one is that the true population mean lies within the interval?

Confidence Interval for the mean

Step-by-step explanation:

Confidence interval is made using the observations of a sample of data obtained from a population, so it is constructed in such a way, that, with a certain level of confidence (this is the statement mentioned in the question), that is, one could have a percentage of probability that the interval, or range around the value obtained, frequently 95%, contains the true value of a population parameter (in this case, the population mean).

It is one way to extract information from a population using a sample of it. This kind of information is what inference statistic is always looking for.

An approximation about how to construct this interval or range:

Select a random sample. For the specific case of a mean, you need to calculate the mean of the sample (sample mean), and, if standard deviation is unknown or not mentioned, also calculate the sample standard deviation. With this information, and acknowledged that these values follows a standard normal distribution (a normal distribution with mean 0 and a standard deviation of 1), represented by random variable Z, one can use all this information to calculate a confidence interval for the mean, with a certain confidence previously choosen (for example, 95%), that the population mean must be in this interval or range around this sample mean.