JustAnswer
Explain the difference between a left-tailed, two-tailed, and right-tailed test. When would you choose a two-tailed test? How might you tell the direction of the test by looking at a pair of hypothesis? How might you tell which direction (or no direction) to make the hypothesis by looking at the problem statement (research question)?
The difference between these tests has to do with where the probability of rejecting the null hypothesis lies with relation to the area under the curve. With a left-tailed test, all the probability is on the left side of the curve. With a right-tailed test, the null hypothesis is only rejected if the test statistic falls into the right side of the curve. And with a two-tailed test, the probabilities are on both sides of the curve.
You can tell the direction by looking at the alternative hypothesis. In a test using the normal or t distribution, the test is two-tailed if the alternative hypothesis says, “not equal to.” It is left-tailed if the alternative hypothesis says “less than,” and right-tailed if it says “greater than.” For example, if I want to prove that plants grow taller with a certain kind of fertilizer, and I know that the previous average height was 10 cm, the alternative hypothesis would be “the average height is greater than 10 cm”. So that would be a right-tailed test.
From the research question, you can tell which it would be if you are only interested in the results of the test in one direction. In almost all cases, a two-tailed test is the most appropriate. In the example above, if I find out that the new fertilizer is actually stunting the growth of the plants, that would be a finding worth reporting!
However, in some cases, we really only want to look at one side of the distribution. For example, suppose I’m an auditor for a truth-in-advertising claim. A certain company has claimed that its product has less than 100 calories per serving, and I need to make sure that the claim is true. In this case, I’d use a one-tailed (left-tailed) test, because I want to prove the claim that is it “less than” 100 calories. If the product doesn’t pass the test, it doesn’t matter to me whether it comes out at 100 calories or greater than 100.
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