Question

Normality Requirement What does it mean when we say that the confidence interval methodsof this section are robust against departures from normality?

Short answer

The confidence interval method will give correct results even if the sample is not from a population that perfectly follows the normal distribution and the sample size is small. The condition that the distribution is approximately symmetric and bell-shaped should be satisfied.

Step-by-step solution

Given information

A sample of 50 Verizon airport data speeds is considered to estimate the value of the mean Verizon airport data speed.

Normality condition of the confidence interval

One of the requirements to construct a confidence interval estimate of the population mean is that either the sample should be from a normally distributed population or the sample size is large.

But this requirement is not very strict and is robust against departures from normality.

This means that if the sample is somewhat bell-shaped, has no outliers, and the sample size is small (between 15 and 30), the confidence interval computed will work well and will be accurate.

Thus, the method of the confidence interval being robust against departures from normality means that a distribution close to the normal distribution will also work if the sample size is small.