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The direction of the alternative hypothesis determines the test type. If the alternative hypothesis uses a greater-than symbol (p > 0.5), a right-tailed test applies with the critical region at the right tail. A less-than symbol (p < 0.5) indicates a left-tailed test with the critical region at the left tail. An inequality symbol (p ≠ 0.5) indicates a two-tailed test with the critical region at both tails equally.

A right-tailed test is used when the alternative hypothesis claims the parameter is greater than the null value, placing the critical region on the right side of the probability distribution. A left-tailed test is used when the alternative hypothesis claims the parameter is less than the null value, placing the critical region on the left side. The direction of the inequality symbol in the alternative hypothesis determines which test applies.

Use a two-tailed test when the alternative hypothesis expresses uncertainty about the direction of difference, stated as an inequality (p ≠ 0.5). In this case, you are testing whether the parameter differs from the null value in either direction. The critical region is split equally between both tails of the probability distribution curve.

Inequality symbols in the alternative hypothesis directly indicate the test direction. The greater-than symbol (>) signals a right-tailed test, the less-than symbol (<) signals a left-tailed test, and the not-equal symbol (≠) signals a two-tailed test. These symbols determine where the critical region falls on the probability distribution and guide the decision-making process.

When testing a claim about population proportion, first establish the null hypothesis as a neutral statement (e.g., p = 0.5). Then formulate the alternative hypothesis using the appropriate inequality symbol. For testing a claim about population proportion, the test type depends on whether you expect the proportion to be greater, less, or simply different from the null value.

The direction of the alternative hypothesis determines the location of the critical region on the probability distribution, which directly affects where you reject the null hypothesis. This directional choice influences the entire decision-making process and determines whether you conduct a one-tailed or two-tailed test, making it fundamental to accurate hypothesis testing.

The null hypothesis provides a neutral baseline statement, while the alternative hypothesis presents an opposing claim with a specific direction. The inequality symbol in the alternative hypothesis—greater than, less than, or not equal—determines whether the test is right-tailed, left-tailed, or two-tailed. Together, they establish the framework for the entire hypothesis test.