If you want to establish a 99.7% confidence interval, how many times should you adjust the standard error?

To establish a 99.7% confidence interval in a statistical context, you are typically referring to the empirical rule, which states that approximately 99.7% of the data in a normal distribution lies within three standard deviations from the mean. In terms of adjusting the standard error, you need to account for the tails of the distribution to ensure that your confidence interval encompasses this range.

When you construct a confidence interval, you add and subtract a margin from the sample mean, and the margin is determined by the standard error multiplied by a critical value from the z distribution. For a 99.7% confidence level, the critical value corresponds to three standard deviations. Thus, you will adjust the standard error three times: once for the upper limit (mean + 3 standard deviations) and once for the lower limit (mean - 3 standard deviations).

This procedure reflects the requirement of encompassing 99.7% of the distribution range when you consider the central tendency (mean) and how far you want to extend outwards to capture the specified confidence level. Therefore, addressing the standard error three times aligns with your goal of establishing a confidence interval that accurately reflects a 99.7% confidence level.