**One-Tailed Test:**

A one-tailed test is a statistical hypothesis test in which the critical region of a distribution is on only one side, either the right or the left.

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The choice of a one-tailed test is typically made based on a directional hypothesis, where the researcher is specifically interested in whether the population parameter is greater than or less than a certain value.

**Example:**Let’s say a researcher wants to test whether a new drug increases the average response time. The null hypothesis ((H_0)) might be that the drug has no effect ((μ = 0)), and the alternative hypothesis ((H_1)) could be that the drug increases response time ((μ > 0)). In this case, a one-tailed test would be appropriate.

**Two-Tailed Test:**

A two-tailed test is a statistical hypothesis test in which the critical region is on both sides of the distribution. It is used when the researcher is interested in whether the population parameter is different from a certain value, but the direction of the difference is not specified.

**Example:**Suppose a researcher wants to test whether a coin is fair (i.e., has an equal probability of landing heads or tails). The null hypothesis ((H_0)) might be that the coin is fair ((p = 0.5)), and the alternative hypothesis ((H_1)) could be that the coin is not fair ((p \neq 0.5)). In this case, a two-tailed test is appropriate because we are interested in deviations from fairness in both directions.

**Summary:**

**One-Tailed Test:**Used when the hypothesis is directional, and the researcher is interested in a specific side of the distribution.**Two-Tailed Test:**Used when the hypothesis is non-directional, and the researcher is interested in deviations from a certain value in either direction.

The choice between a one-tailed and two-tailed test depends on the specific research question and hypothesis being investigated.