Final answer:
The term zα/2 (σ/√n) refers to the margin of error in the context of constructing confidence intervals for a population mean when using a sample statistic, assuming a normal distribution and known standard deviation.
Step-by-step explanation:
The term zα/2 (σ/√n) describes the margin of error in statistics, specifically when constructing confidence intervals for estimating a population mean. This term is part of a formula that is used when you have a normally distributed population with a known standard deviation, and you want to create a confidence interval for the population mean based on a sample statistic.
The zα/2 value is the z-score that corresponds to the desired confidence level, found in the standard normal distribution table, and represents the critical value or cutoff where the tails of the distribution begin. It is the number of standard deviations away from the mean needed to capture the central area under the curve which equals the confidence level. The σ represents the population standard deviation, and n is the sample size.
By dividing σ by the square root of n, you get what is known as the standard error of the mean, which adjusts the standard deviation of the population for the size of the sample. When you multiply the z-score by the standard error, you obtain the margin of error, which gives you a range indicating where the true population mean is likely to fall with the given level of confidence.