Lecture 6 - Ch 9b - One-Tail Hypothesis Testing

When the null hypothesis is that the current population mean equals the historic mean and the alternative hypothesis is that it does not equal the historic mean, we construct a two-tailed rejection region on either side of the distribution. We reject H₀ is the sample mean is too high to too low.

However, that's not always the case. Sometimes, our null hypothesis is that the mean is at least equal to the historic mean (but possibly larger). In such a case, we would only reject H₀ if it was less than the lower bound (critical value) of the non-rejection region.




Similarly, sometimes our H₀ is that the mean is at most equal to the historic mean (but possibly smaller). In this a case, we would only reject H₀ if it was greater than the lower bound (critical value) of the non-rejection region.

The methodology for doing a one-tail hypothesis test is almost the same as for the two-tail test. The major difference is that our entire rejection region is on one side of the distribution. Therefore, when you set the level of significance, alpha, and the confidence level, (1-alpha)x100, that reflects only one side of the distribution.

Practically speaking, it means that when you compare the z-score of the sample mean to the critical value, the critical value comes from z_alpha instead of z_alpha/2.

The same logic applies to the p-value approach.