9.5:
Types of Hypothesis Testing
Consider the example of testing a claim about the proportion of healthy and scabbed apples from a cultivar.
In this case, the null hypothesis is stated as the cultivar produces an equal number of healthy and scabbed apples.
Here, the alternative hypothesis can be expressed in three different ways, and based on that, the type of hypothesis test is decided.
One way to state the alternative hypothesis is that the cultivar produces more healthy apples than scabbed apples. In this case, the right-tailed hypothesis test is applicable as the critical region would be at the right tail of the distribution.
When we state that the cultivar produces less number of healthy apples, the critical region would be at the left tail of the distribution. Here, the left-tailed hypothesis test is applicable.
In case of uncertainty of the direction of the hypothesis, we may state that the cultivar produces an unequal number of healthy and scabbed apples. As the critical region would be at both the tails equally, the two-tailed hypothesis test would be applicable.
9.5:
Types of Hypothesis Testing
There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed.
When the null and alternative hypotheses are stated, it is observed that the null hypothesis is a neutral statement against which the alternative hypothesis is tested. The alternative hypothesis is a claim that instead has a certain direction. If the null hypothesis claims that p = 0.5, the alternative hypothesis would be an opposing statement to this and can be put either p > 0.5, p < 0.5, or p ≠ 0.5. In all these alternative hypotheses statements, the inequality symbols indicate the direction of the hypothesis. Based on the direction mentioned in the hypothesis, the type of hypothesis test can be decided for the given population parameter.
When the alternative hypothesis claims p > 0.5 (notice the 'greater than symbol), the critical region would fall at the right side of the probability distribution curve. In this case, the right-tailed hypothesis test is used.
When the alternative hypothesis claims p < 0.5 (notice the 'less than' symbol), the critical region would fall at the left side of the probability distribution curve. In this case, the left-tailed hypothesis test is used.
In the case of the alternative hypothesis p ≠ 0.5, a definite direction cannot be decided, and therefore the critical region falls at both the tails of the probability distribution curve. In this case, the two-tailed test should be used.