Ha

Definition

In the context of statistical hypothesis testing, Ha, or the alternative hypothesis, represents the statement that the researcher believes to be true. It is the hypothesis that is accepted if the null hypothesis is rejected based on the available evidence from the sample data.

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 null hypothesis (H0) and the alternative hypothesis (Ha) are always mutually exclusive, meaning that if one is true, the other must be false.
3. In a two-tailed test, the alternative hypothesis is that the parameter is not equal to the hypothesized value, whereas in a one-tailed test, the alternative hypothesis is that the parameter is greater than or less than the hypothesized value.
4. The p-value is used to determine the strength of the evidence against the null hypothesis, with a smaller p-value indicating stronger evidence.
5. The choice between the null and alternative hypotheses is made based on the p-value and the predetermined significance level (α), which represents the maximum acceptable probability of rejecting the null hypothesis when it is true.

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 mutually exclusive statements about a population parameter. The null hypothesis represents the claim or assumption that the researcher wants to test, while the alternative hypothesis is the statement that the researcher believes to be true. The goal of hypothesis testing is to determine whether the available evidence from the sample data is strong enough to reject the null hypothesis in favor of the alternative hypothesis.
• Describe the role of the p-value in the decision-making process when testing the significance of a correlation coefficient.
  • The p-value is a crucial component in testing the significance of a correlation coefficient. It represents the probability of obtaining a test statistic at least as extreme as the one observed, given that the null hypothesis (that the correlation coefficient is equal to zero) is true. The p-value is compared to the predetermined significance level (α) to determine whether the evidence is strong enough to reject the null hypothesis and conclude that the correlation coefficient is significantly different from zero. A p-value less than the significance level provides evidence to support the alternative hypothesis, which states that the correlation coefficient is not equal to zero.
• Analyze the implications of a Type I error (rejecting the null hypothesis when it is true) and a Type II error (failing to reject the null hypothesis when it is false) in the context of hypothesis testing.
  • A Type I error occurs when the null hypothesis is rejected when it is actually true, while a Type II error occurs when the null hypothesis is not rejected when it is actually false. The implications of these errors are significant in hypothesis testing. A Type I error can lead to the conclusion that there is a significant effect or difference when in reality, there is none, potentially resulting in unnecessary actions or interventions. Conversely, a Type II error can lead to the conclusion that there is no significant effect or difference when in reality, there is one, potentially leading to missed opportunities or failing to address an important issue. Understanding the trade-offs between these two types of errors is crucial in designing and interpreting hypothesis tests, as researchers must balance the risks of making these errors based on the context and the consequences of each type of error.

Related terms

Null Hypothesis (H0): The null hypothesis is the statement of no effect or no difference, which is assumed to be true unless the statistical evidence strongly suggests otherwise.

Statistical Significance: Statistical significance refers to the probability that the observed result would have occurred by chance if the null hypothesis is true. It is used to determine whether the evidence is strong enough to reject the null hypothesis.

P-value: The p-value is the probability of obtaining a test statistic at least as extreme as the one observed, given that the null hypothesis is true. It is used to assess the strength of the evidence against the null hypothesis.