$H_0$

Definition

$H_0$, also known as the null hypothesis, is a statistical term that represents the initial assumption or claim made about a population parameter. It is the hypothesis that is tested against the available evidence to determine if it should be rejected in favor of an alternative hypothesis.

5 Must Know Facts For Your Next Test

1. The null hypothesis, $H_0$, represents the status quo or the claim that there is no significant difference or relationship between the variables being studied.
2. In the context of rare events (Chapter 9.4), $H_0$ is often used to test the assumption that an event is unlikely to occur by chance alone.
3. When testing the significance of a correlation coefficient (Chapter 12.3), $H_0$ states that there is no significant correlation between the two variables.
4. In the comparison of chi-square tests (Chapter 11.5), $H_0$ is used to test the assumption that the observed frequencies in a contingency table are not significantly different from the expected frequencies.
5. The decision to reject or fail to reject the null hypothesis is based on the statistical evidence provided by the sample data and the level of significance chosen for the test.

Review Questions

• Explain the role of the null hypothesis, $H_0$, in the context of testing for rare events.
  • In the context of rare events (Chapter 9.4), the null hypothesis, $H_0$, represents the assumption that the observed event is unlikely to occur by chance alone. The statistical test is designed to determine whether the evidence from the sample data is strong enough to reject this null hypothesis and conclude that the event is indeed rare and not due to random chance. The decision to reject or fail to reject $H_0$ is crucial in understanding the significance of the rare event and its potential implications.
• Describe how the null hypothesis, $H_0$, is used in the comparison of chi-square tests (Chapter 11.5).
  • In the comparison of chi-square tests (Chapter 11.5), the null hypothesis, $H_0$, is used to test the assumption that the observed frequencies in a contingency table are not significantly different from the expected frequencies. The chi-square test statistic is calculated to determine the likelihood of observing the given frequencies if the null hypothesis is true. If the test statistic is large enough to indicate a low probability of the observed frequencies under $H_0$, the null hypothesis is rejected, suggesting that the observed and expected frequencies are significantly different.
• Analyze the role of the null hypothesis, $H_0$, in testing the significance of the correlation coefficient (Chapter 12.3).
  • When testing the significance of the correlation coefficient (Chapter 12.3), the null hypothesis, $H_0$, states that there is no significant correlation between the two variables. The statistical test is designed to determine whether the sample data provides sufficient evidence to reject this null hypothesis and conclude that there is a significant correlation between the variables. The decision to reject or fail to reject $H_0$ is crucial in understanding the strength and direction of the relationship between the variables and its potential implications for the research or problem being investigated.

Related terms

Null Hypothesis: The null hypothesis is the initial statement or claim made about a population parameter that is tested for statistical significance.

Alternative Hypothesis: The alternative hypothesis is the statement that contradicts the null hypothesis and is accepted if the null hypothesis is rejected.

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.