# Left-Tailed, Two-Tailed, and Right-Tailed Testing

Explain the difference between a left-tailed, two-tailed, and right-tailed test. When would we choose a two-tailed test?

How can we tell the direction of the test by looking at a pair of hypothesis?

How can we tell which direction (or no direction) to make the hypothesis by looking at the problem statement (research question)?

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#### Solution Preview

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In every hypothesis testing problem, there is a pair of competing statistical hypotheses: the null hypothesis and the alternative hypothesis. The Null hypothesis, denoted by H0, is typically a clear statement of equality: the unknown population parameter Î¸ is equal to some specific constant value Î¸0 (the hypothesized value of population parameter Î¸).

In symbolic form this hypothesis is written as H0 : Î¸ = Î¸0

The null hypothesis is also called the no-difference hypothesis, because it states that there is no difference between Î¸ and Î¸0

The alternative hypothesis, denoted by H1, is an assumption about Î¸ that differs from H0.

If the alternative hypothesis is left directional, in other words, if we test the null hypothesis H0 : Î¸ = Î¸0Â¬ against the alternative hypothesis

H1 : Î¸ < Î¸0Â¬Â¬, then this hypothesis test is ...

#### Solution Summary

This response differentiates between the left-tailed, two-tailed, and right-tailed test. It also explains how to tell the direction of a test by looking at the hypotheses.