What is the difference between a one-tailed and a two-tailed test?

• A. A one-tailed test checks for deviations in both directions
• B. A two-tailed test checks for deviations in one direction
• C. A one-tailed test checks for deviations in one direction while a two-tailed test checks for both directions
• D. Both tests check for deviations in all directions

Answer: (C)

The distinction between a one-tailed test and a two-tailed test lies primarily in the directionality of the hypothesis being tested. A one-tailed test is designed to determine if a parameter is either greater than or less than a certain value, focusing on one specific direction of deviation from the hypothesized value. For example, if a researcher wants to test whether a new drug is more effective than an existing treatment, they would set up a one-tailed test to check for an increase in effectiveness only.

In contrast, a two-tailed test assesses deviations in both directions, meaning it tests for the possibility that a parameter is either greater than or less than a certain value. This approach is appropriate when the researcher is interested in any significant deviation from the hypothesized value, regardless of direction. For instance, if the null hypothesis states that a new teaching method has no effect on student performance, a two-tailed test would evaluate both the potential for improved performance and the potential for degraded performance.

Thus, the correct answer accurately captures the essence of the tests: a one-tailed test checks for deviations in one direction, while a two-tailed test checks for deviations in both directions. Understanding this fundamental difference is crucial for appropriately selecting which statistical test to use