How would you create a 95% confidence interval starting from the sample average?

To create a 95% confidence interval starting from the sample average, you correctly would add and subtract twice the standard error. This is based on the properties of the normal distribution and the concept of confidence intervals in statistics.

When constructing a 95% confidence interval, we aim to capture the population parameter (like the mean) within the interval created by our sample statistic. The standard error represents the variability of the sample mean estimation, and by multiplying it by two, we leverage the empirical rule, which states that approximately 95% of the data falls within two standard deviations (or in this case, two standard errors) of the mean for a normally distributed variable.

Therefore, the interval is calculated as the sample mean minus two times the standard error and the sample mean plus two times the standard error. This results in a range within which we can be 95% confident that the true population mean lies. Using any other multiplier, such as one or three, would not yield the correct confidence level for a 95% interval, leading to an inaccurate representation of the population mean's likely range based on the sample data.