Draw the graph of a two-tailed test.

Name: Problem 36, Chapter 9: Introductory Business Statistics
Uploaded: 2020-02-22T19:37:40-08:00
Duration: 1 min 18 s
Channel: Lucas Everson
Description: Draw the graph of a two-tailed test.

Key Concepts

Two-Tailed Test

A two-tailed test is a statistical hypothesis test in which the rejection region for the null hypothesis is split equally between the two tails of the probability distribution. This test is used when deviations in both directions—either higher or lower than the expected value—might indicate that the null hypothesis should be rejected. It is applicable when the direction of the effect is not specified or when both possibilities are of interest.

Significance Level

The significance level, commonly denoted as alpha (?), represents the probability of making a Type I error, which is the error of rejecting a true null hypothesis. In a two-tailed test, the total significance level is divided equally between the two tails of the distribution. This means that each tail has an area of ?/2, defining the boundaries of the critical regions.

Test Statistic Distribution

The test statistic distribution is the theoretical probability distribution that the test statistic follows under the null hypothesis. Common examples include the normal distribution and the t-distribution. In a two-tailed test, this distribution is used to determine the critical values beyond which the null hypothesis is rejected, as these values represent the cutoff points corresponding to the ?/2 probability in each tail.

Graphical Representation

A graphical representation of a two-tailed test typically consists of a bell-shaped curve (such as the normal or t-distribution) with the curve centered on the null hypothesis parameter value. The critical regions are marked on both ends of the curve, each with an area equal to ?/2. This shading illustrates the regions where, if the test statistic falls, the null hypothesis would be rejected, effectively visualizing the potential for significant differences in either direction.

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