What is the standard format for an interval estimate of a population mean?

The standard format for an interval estimate of a population mean, when the sample size is small or when the population standard deviation is unknown, involves using the t-distribution. The expression x̅ +/- t(lower α/2)(s/SQRT(n)) captures this approach perfectly, where x̅ represents the sample mean, t(lower α/2) is the critical value from the t-distribution corresponding to the chosen level of confidence and degrees of freedom, s is the sample standard deviation, and n is the sample size.

Using the t-distribution is appropriate in these cases because it accounts for the additional uncertainty introduced when estimating the population standard deviation from a sample, especially when the sample size is small (typically n < 30). This leads to more accurate interval estimates of the population mean compared to using the normal distribution, which is what would be done if the population standard deviation were known or the sample size were sufficiently large.

The other options utilize different parameters or statistical principles that are not appropriate for a standard interval estimate of a population mean. For instance, using the z-score in the first option assumes that the population standard deviation is known, which is not the case here. The third option uses a misapplied formula that does not