Question

Explain why considering outliers is important when you are conducting a one-mean z-test.

Short answer

The test statistic, z may be unduly effected by outliers since the sample mean is not resistant to outliers. That is why we consider outliers when we are conducting a one-mean z-test.

Step-by-step solution

Step 1. Consider one-mean z-test.

Consider a one-mean z-test procedure, the test statistics is given below,

$z=\frac{\overline{x}-\mu }{{\displaystyle \frac{\sigma }{\sqrt{n}}}}$

Step 2. Consider the above test statistics.

Consider the above test statistics,

Which depends on the sample mean, $\overline{x}$.

Therefore, the test statistic, z may be unduly effected by outliers since the sample mean is not resistant to outliers. That is why we consider outliers when we are conducting a one-mean z-test.