Ha

Definition

In the context of hypothesis testing, Ha, or the alternative hypothesis, represents the statement that the researcher believes to be true. It is the complement of the null hypothesis (H0) and is the hypothesis that the researcher aims to provide evidence for through statistical analysis.

5 Must Know Facts For Your Next Test

1. The alternative hypothesis (Ha) is the statement that the researcher believes to be true and wants to provide evidence for.
2. The alternative hypothesis is the complement of the null hypothesis, meaning that if the null hypothesis is false, the alternative hypothesis must be true.
3. The alternative hypothesis can take different forms, such as a statement about a difference, a relationship, or a specific value.
4. The alternative hypothesis is used to determine the direction of the test, which can be one-tailed (directional) or two-tailed (non-directional).
5. The strength of the evidence against the null hypothesis is determined by the p-value, which is the probability of obtaining the observed test statistic (or a more extreme value) under the assumption that the null hypothesis is true.

Review Questions

• Explain the relationship between the null hypothesis (H0) and the alternative hypothesis (Ha).
  • The null hypothesis (H0) and the alternative hypothesis (Ha) are complementary statements in a hypothesis test. The null hypothesis represents the statement of no significant difference or relationship, while the alternative hypothesis is the statement that the researcher believes to be true. If the null hypothesis is rejected, it provides evidence in favor of the alternative hypothesis. The two hypotheses are mutually exclusive, meaning that if one is true, the other must be false.
• Describe how the alternative hypothesis (Ha) is used to determine the direction of the hypothesis test.
  • The form of the alternative hypothesis (Ha) determines the direction of the hypothesis test. If the alternative hypothesis states a specific direction, such as a greater than or less than relationship, the test is considered one-tailed. In this case, the critical region for rejecting the null hypothesis is located on one side of the sampling distribution. If the alternative hypothesis is non-directional, such as a statement about a difference or a relationship without a specific direction, the test is considered two-tailed, and the critical region is located on both sides of the sampling distribution.
• Explain the role of the p-value in the decision to reject or fail to reject the null hypothesis (H0) in favor of the alternative hypothesis (Ha).
  • The p-value is the probability of obtaining the observed test statistic (or a more extreme value) under the assumption that the null hypothesis (H0) is true. The p-value is compared to the predetermined significance level (α) to determine whether to reject or fail to reject the null hypothesis. If the p-value is less than or equal to the significance level, the null hypothesis is rejected, and the alternative hypothesis (Ha) is supported. Conversely, if the p-value is greater than the significance level, the null hypothesis is not rejected, and there is insufficient evidence to conclude that the alternative hypothesis is true.

Related terms

Null Hypothesis (H0): The null hypothesis is a statement that there is no significant difference or relationship between the variables being studied. It is the hypothesis that the researcher aims to disprove through the statistical analysis.

Significance Level (α): The significance level is the probability threshold used to determine whether to reject the null hypothesis. It represents the maximum acceptable probability of making a Type I error, which is the error of rejecting the null hypothesis when it is true.

Test Statistic:

The test statistic is a numerical value calculated from the sample data that is used to determine whether the null hypothesis should be rejected or not. The test statistic is compared to a critical value to make this decision.