To get a 68% confidence interval, what should you do with the sample average?

To compute a 68% confidence interval, you would typically use the concept of adding and subtracting one standard error from the sample mean. This is grounded in the properties of the normal distribution, particularly that approximately 68% of the data falls within one standard deviation of the mean in a normal distribution.

When you calculate the standard error from your sample data, you can obtain the confidence interval by taking the sample average—also known as the sample mean—and modifying it by the standard error. Since the goal is to capture approximately 68% of the data around the mean, incorporating one standard error on either side of the mean is sufficient. This approach reflects the empirical rule regarding the spread of data in a normal distribution, allowing us to estimate the range in which we expect the true population mean to fall with 68% certainty.

In contrast, adding and subtracting two, three, or four standard errors would create wider intervals, corresponding to higher levels of confidence such as 95% or 99.7%. These intervals would encompass a significantly larger portion of the data, but they are not needed to achieve the target of 68% confidence, making them unnecessary for this particular question.