8.5 upper and lower tail

Lower-tail test

Upper-tail test

This means that only values for the sample mean that are less than 50 can lead us to reject the null hypothesis in favour of the alternative.

Critical value

Critical value

H0: μ = 50 OR μ ≥ 50 H1: μ < 50

H0: μ = 50 OR μ ≤ 50 H1: μ > 50

Now only α not

This means that only values for the sample mean that are greater than 50 can lead us to reject the null hypothesis in favour of the alternative.

Now only α not

• Remember our alternative hypothesis for a two-tailed test contain a not equal sign (≠).
• However, when the alternative hypothesis focuses on one particular direction we have a one-tailed test.
• For both the lower and upper tail tests, you can either use an = sign in the null hypothesis, or you can use ≤ or ≥