The alternative hypothesis is a statement that contradicts the null hypothesis in a statistical hypothesis test. It represents the researcher's belief or prediction about the relationship between the variables being studied.
5 Must Know Facts For Your Next Test
The alternative hypothesis is denoted by $H_1$ or $H_a$, while the null hypothesis is denoted by $H_0$.
The alternative hypothesis must be a specific, directional statement that indicates the direction of the expected difference or relationship.
The choice of the alternative hypothesis depends on the research question and the researcher's expectations or predictions.
The alternative hypothesis is the hypothesis that the researcher hopes to support or provide evidence for through the statistical analysis.
The alternative hypothesis is used to determine the decision rule for the hypothesis test, which is based on the probability distribution of the test statistic under the null hypothesis.
Review Questions
Explain the role of the alternative hypothesis in a statistical hypothesis test.
The alternative hypothesis plays a crucial role in a statistical hypothesis test. It represents the researcher's belief or prediction about the relationship between the variables being studied, and it contradicts the null hypothesis. The alternative hypothesis is used to determine the decision rule for the hypothesis test, which is based on the probability distribution of the test statistic under the null hypothesis. The goal of the hypothesis test is to either reject the null hypothesis in favor of the alternative hypothesis or fail to reject the null hypothesis, depending on the evidence provided by the sample data.
Describe the characteristics of a well-formulated alternative hypothesis.
A well-formulated alternative hypothesis should be a specific, directional statement that indicates the expected direction of the difference or relationship between the variables. It must be mutually exclusive with the null hypothesis, meaning that if the alternative hypothesis is true, the null hypothesis must be false. The alternative hypothesis should also be based on the researcher's expectations or predictions, which are informed by existing theory, previous research, or the specific research question being investigated.
Analyze the relationship between the alternative hypothesis and the decision-making process in a hypothesis test.
The alternative hypothesis is crucial in determining the decision-making process for a hypothesis test. The decision rule, which specifies the criteria for rejecting or failing to reject the null hypothesis, is based on the probability distribution of the test statistic under the null hypothesis. The alternative hypothesis is used to specify the direction of the expected difference or relationship, which in turn determines the appropriate one-tailed or two-tailed test and the corresponding critical values. The strength of the evidence provided by the sample data is then evaluated against the decision rule to make the final decision, either rejecting the null hypothesis in favor of the alternative hypothesis or failing to reject the null hypothesis.
Related terms
Null Hypothesis: The null hypothesis is a statement of no difference or no effect, which serves as the starting point for a statistical hypothesis test.
Type I Error: A Type I error occurs when the null hypothesis is true, but it is incorrectly rejected, leading to a false positive conclusion.
Type II Error: A Type II error occurs when the null hypothesis is false, but it is incorrectly not rejected, leading to a false negative conclusion.