Question

In computing upper and lower limit, one needs to multiply the relevant z score (e.g., 1.96 for 95% and 2.58 for 99% CI) with SE before adding/subtracting that from the mean. Explain the logic behind this formula.

Answer 1

The formula involving z-scores, SE, and the mean is used to calculate the upper and lower limits of a confidence interval (CI). The z-score represents the number of standard deviations the desired confidence level extends from the mean.

Step-by-step explanation:

The logic behind multiplying the relevant z-score with the standard error (SE) and adding/subtracting it from the mean is to calculate the upper and lower limits of a confidence interval (CI). The z-score represents the number of standard deviations the desired confidence level extends from the mean. By multiplying the z-score with the SE, we determine the margin of error. Adding/subtracting this margin of error from the mean gives us the upper and lower limits of the CI.

For example, suppose we want to construct a 95% CI. The z-score for a 95% CI is 1.96. If the mean is 50 and the SE is 5, we multiply 1.96 by 5 to get the margin of error, which is 9.8. Adding/subtracting this margin of error from the mean gives us an upper limit of 59.8 and a lower limit of 40.2.