key term - $H_1$

Definition

$H_1$ is the alternative hypothesis in a statistical hypothesis test. It represents the statement that the researcher believes to be true, in contrast to the null hypothesis ($H_0$), which is the statement the researcher is trying to disprove.

5 Must Know Facts For Your Next Test

1. $H_1$ represents the researcher's belief or claim about the population parameter or relationship being studied.
2. The alternative hypothesis is usually denoted as $H_1$ or $H_a$, and it is the hypothesis the researcher hopes to support through the statistical analysis.
3. In the context of rare events (9.4), $H_1$ would represent the belief that the probability of a rare event occurring is greater than a specified threshold.
4. When testing the significance of a correlation coefficient (12.3), $H_1$ would represent the belief that the population correlation coefficient is not equal to zero.
5. The decision to reject or fail to reject $H_0$ is based on the evidence provided by the sample data and the chosen significance level.

Review Questions

• Explain the relationship between the null hypothesis ($H_0$) and the alternative hypothesis ($H_1$) in a statistical hypothesis test.
  • The null hypothesis ($H_0$) and the alternative hypothesis ($H_1$) are complementary statements in a statistical hypothesis test. The null hypothesis represents the default or status quo position that the researcher is trying to disprove, while the alternative hypothesis ($H_1$) represents the researcher's belief or claim about the population parameter or relationship being studied. The decision to reject or fail to reject the null hypothesis is based on the evidence provided by the sample data and the chosen significance level ($\alpha$).
• Describe how the alternative hypothesis ($H_1$) is used in the context of testing for rare events (9.4) and testing the significance of a correlation coefficient (12.3).
  • In the context of rare events (9.4), the alternative hypothesis ($H_1$) would represent the belief that the probability of a rare event occurring is greater than a specified threshold. The researcher would then use statistical analysis to determine whether the sample data provides sufficient evidence to reject the null hypothesis ($H_0$) and support the alternative hypothesis ($H_1$). Similarly, when testing the significance of a correlation coefficient (12.3), the alternative hypothesis ($H_1$) would represent the belief that the population correlation coefficient is not equal to zero. The researcher would use the sample data to calculate a test statistic and determine whether to reject the null hypothesis ($H_0$) in favor of the alternative hypothesis ($H_1$).
• Analyze the role of the alternative hypothesis ($H_1$) in the overall decision-making process of a statistical hypothesis test.
  • The alternative hypothesis ($H_1$) plays a crucial role in the decision-making process of a statistical hypothesis test. It represents the researcher's belief or claim about the population parameter or relationship being studied, and the goal of the statistical analysis is to determine whether the sample data provides sufficient evidence to reject the null hypothesis ($H_0$) in favor of the alternative hypothesis ($H_1$). The decision to reject or fail to reject the null hypothesis is based on the calculated test statistic and the chosen significance level ($\alpha$). If the test statistic falls in the rejection region, the researcher can conclude that the sample data supports the alternative hypothesis ($H_1$) and reject the null hypothesis ($H_0$). This decision-making process is crucial in drawing valid conclusions about the population and making informed decisions based on the statistical analysis.

Related terms

Null Hypothesis ($H_0$): The null hypothesis is the statement that the researcher is trying to disprove. It represents the default or status quo position that there is no significant difference or relationship.

Significance Level ($\alpha$): The significance level is the probability threshold set by the researcher to determine whether to reject the null hypothesis in favor of the alternative hypothesis.

Test Statistic:

The test statistic is a numerical value calculated from the sample data that is used to determine whether to reject or fail to reject the null hypothesis.