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Hypothesis Testing: Explain the Difference between a Left-Tailed, Two-Tailed, and Right-Tailed Test

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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 hypotheses? 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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(1) Explain the difference between a left-tailed, two-tailed, and right-tailed test. When would we choose a two-tailed test?

The three types of tests are very similar.

When you want to test whether a parameter (mean/percentage/correlation/etc.) of a population is greater than a given number or if it is greater than the mean/percentage/correlation of another population, you use a right-tailed test. In this case, you reject the null hypothesis if the observed statistic (the value of z, t, r, etc. that you calculate) is larger than the positive critical value (i.e. if the observed z is greater than 1.96).

When you want to test whether a parameter of a population is less than a given number or if it is less than the parameter of another population, you use a left-tailed test. In this case, you reject the null hypothesis if the observed statistic (the value of z, t, r, etc. that ...

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