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

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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)?

#### Solution Preview

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 θ is equal to some specific constant value θ0 (the hypothesized value of population parameter θ).

In symbolic form this hypothesis is written as H0 : θ = θ0

The null hypothesis is also called the no-difference hypothesis, because it states that there is no difference between θ and θ0

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

If the alternative hypothesis is left directional, in other words, if we test the null hypothesis H0 : θ = θ0¬ against the alternative hypothesis
H1 : θ < θ0¬¬, 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.

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