Ha

Definition

In the context of hypothesis testing, Ha represents the alternative hypothesis, which is the statement that the researcher believes to be true. The alternative hypothesis is the complement of the null hypothesis, and it is the hypothesis that the researcher aims to provide evidence for through the 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 through the statistical analysis.
2. The alternative hypothesis is the complement of the null hypothesis, meaning that if the null hypothesis is false, then the alternative hypothesis must be true.
3. In a two-tailed test, the alternative hypothesis takes the form of Ha: θ ≠ θ0, where θ represents the parameter of interest and θ0 is the hypothesized value of the parameter.
4. In a one-tailed test, the alternative hypothesis can take the form of Ha: θ > θ0 (right-tailed test) or Ha: θ < θ0 (left-tailed test).
5. The decision to reject or fail to reject the null hypothesis is based on the comparison of the test statistic to the critical value, which is determined by the significance level (α) and the sampling distribution.

Review Questions

• Explain the relationship between the null hypothesis (H0) and the alternative hypothesis (Ha) in the context of hypothesis testing.
  • The null hypothesis (H0) and the alternative hypothesis (Ha) are complementary statements in hypothesis testing. The null hypothesis represents the initial claim or assumption that the researcher believes to be true, while the alternative hypothesis is the statement that the researcher wants to provide evidence for through the statistical analysis. If the null hypothesis is rejected, then the alternative hypothesis is accepted as true. Conversely, if the null hypothesis is not rejected, then the alternative hypothesis is not supported by the data.
• Describe the different forms of the alternative hypothesis (Ha) in one-tailed and two-tailed tests.
  • In a two-tailed test, the alternative hypothesis takes the form of Ha: θ ≠ θ0, where θ represents the parameter of interest and θ0 is the hypothesized value of the parameter. This means that the researcher is interested in determining whether the true value of the parameter is different from the hypothesized value, without specifying the direction of the difference. In a one-tailed test, the alternative hypothesis can take the form of Ha: θ > θ0 (right-tailed test) or Ha: θ < θ0 (left-tailed test), where the researcher is interested in determining whether the true value of the parameter is greater than or less than the hypothesized value, respectively.
• Explain how the decision to reject or fail to reject the null hypothesis is made based on the comparison of the test statistic and the critical value.
  • The decision to reject or fail to reject the null hypothesis is based on the comparison of the test statistic, which is a numerical value calculated from the sample data, and the critical value, which is determined by the significance level (α) and the sampling distribution. If the test statistic falls within the critical region (the region where the null hypothesis is rejected), then the null hypothesis is rejected, and the alternative hypothesis is accepted as true. Conversely, if the test statistic falls outside the critical region, then the null hypothesis is not rejected, and there is not enough evidence to support the alternative hypothesis.

Related terms

Null Hypothesis (H0): The null hypothesis is the initial statement that the researcher believes to be true, and it is the hypothesis that will be tested against the alternative hypothesis.

Significance Level (α): The significance level is the maximum probability of rejecting the null hypothesis when it is actually true, which is also known as the Type I error.

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.