Question

what is the differnce between a one tail z test and a two tail z test? When should we use one over the other?

Answer 1

If the alternative hypothesis in a z-test consists of ‘less than’ or ‘greater than’ type of inequality, then this z-test is said to be a one tailed z test.

If the alternative hypothesis in a z-test consists of ‘not equal to’ type of inequality, then this z-test is said to be a two tailed z-test.

For example:

One tail z test:

H₀: µ = 5 vs. H_a­: µ > 5

Or

H₀: µ = 5 vs. H_a­: µ < 5

Two tail z test:

H₀: µ = 5 vs. H_a­: µ ≠ 5

We should use one tail z-test when alternative hypothesis or research hypothesis wants to show sample mean is less than or greater than that of population mean.

We should use two tail z-test when alternative hypothesis or research hypothesis wants to show sample mean is not equal to that of population mean.