Reject

Definition

In the context of statistical hypothesis testing, to reject a null hypothesis means that the observed data provides sufficient evidence to conclude that the null hypothesis is false. The decision to reject the null hypothesis is made based on the results of a statistical test, which determines the likelihood of obtaining the observed data if the null hypothesis is true.

5 Must Know Facts For Your Next Test

1. Rejecting the null hypothesis means that the observed data provides strong evidence against the null hypothesis, suggesting that the alternative hypothesis is more likely to be true.
2. The decision to reject the null hypothesis is based on the comparison of the test statistic (e.g., t-statistic, z-statistic) to a critical value or the p-value to the chosen significance level.
3. Rejecting the null hypothesis does not necessarily mean that the alternative hypothesis is true; it only means that the observed data is unlikely to have occurred if the null hypothesis were true.
4. The probability of rejecting the null hypothesis when it is true is called the Type I error, and the probability of failing to reject the null hypothesis when it is false is called the Type II error.
5. The significance level, denoted as α, represents the maximum acceptable probability of making a Type I error (rejecting the null hypothesis when it is true).

Review Questions

• Explain the process of rejecting the null hypothesis in the context of hypothesis testing.
  • The process of rejecting the null hypothesis involves calculating a test statistic (e.g., t-statistic, z-statistic) based on the observed data and comparing it to a critical value or calculating the p-value. If the test statistic falls in the rejection region (i.e., beyond the critical value) or the p-value is less than the chosen significance level (e.g., α = 0.05), the null hypothesis is rejected. Rejecting the null hypothesis suggests that the observed data provides sufficient evidence to conclude that the alternative hypothesis is more likely to be true.
• Describe the relationship between the significance level, Type I error, and the decision to reject the null hypothesis.
  • The significance level, denoted as α, represents the maximum acceptable probability of making a Type I error, which is the error of rejecting the null hypothesis when it is true. The smaller the significance level, the less likely the researcher is to reject the null hypothesis when it is true. For example, if the significance level is set at α = 0.05, the researcher is willing to accept a 5% chance of rejecting the null hypothesis when it is true. The decision to reject the null hypothesis is made when the p-value is less than the chosen significance level, indicating that the observed data is unlikely to have occurred if the null hypothesis were true.
• Explain the implications of rejecting the null hypothesis in the context of 9.1 Null and Alternative Hypotheses.
  • In the context of 9.1 Null and Alternative Hypotheses, rejecting the null hypothesis means that the observed data provides sufficient evidence to conclude that the alternative hypothesis is more likely to be true. This implies that there is a significant difference or relationship between the variables being studied, as specified in the alternative hypothesis. Rejecting the null hypothesis is an important step in the hypothesis testing process, as it allows the researcher to draw conclusions about the population parameters or the relationship between the variables of interest. The decision to reject the null hypothesis has important implications for the researcher's understanding of the phenomenon being studied and can inform further research or decision-making.

Related terms

Null Hypothesis: The null hypothesis is a statement that there is no significant difference or relationship between the variables being studied. It is the hypothesis that the researcher is trying to disprove or reject.

Alternative Hypothesis: The alternative hypothesis is the statement that there is a significant difference or relationship between the variables being studied. If the null hypothesis is rejected, the alternative hypothesis is accepted as true.

p-value: The p-value is the probability of obtaining the observed data or more extreme data, given that the null hypothesis is true. If the p-value is less than the chosen significance level, the null hypothesis is rejected.