Critical Value

Definition

The critical value is a threshold value in statistical analysis that determines whether to reject or fail to reject a null hypothesis. It is a key concept in hypothesis testing and is used to establish the boundaries for statistical significance in various statistical tests.

5 Must Know Facts For Your Next Test

1. The critical value is used to compare the test statistic to determine if the null hypothesis should be rejected or not.
2. The critical value depends on the chosen significance level, the distribution of the test statistic, and the degrees of freedom.
3. In a two-tailed test, the critical value represents the boundary values that the test statistic must fall outside of to reject the null hypothesis.
4. The critical value is used in confidence interval calculations to determine the range of values that are likely to contain the true population parameter.
5. The critical value is an essential component in hypothesis testing, as it allows researchers to make informed decisions about the significance of their findings.

Review Questions

• Explain the role of the critical value in hypothesis testing for a single population mean using the normal distribution (8.1).
  • In the context of 8.1 A Single Population Mean Using the Normal Distribution, the critical value is used to determine the threshold for rejecting the null hypothesis. The critical value is obtained from the standard normal distribution and is based on the chosen significance level and whether the test is one-tailed or two-tailed. The test statistic is then compared to the critical value, and if the test statistic falls in the rejection region (beyond the critical value), the null hypothesis is rejected, indicating that the population mean is significantly different from the hypothesized value.
• Describe how the critical value is used in the hypothesis testing of a population proportion (8.3).
  • In the context of 8.3 A Population Proportion, the critical value is used to establish the boundaries for the rejection region when testing a hypothesis about a population proportion. The critical value is obtained from the standard normal distribution and is based on the chosen significance level and whether the test is one-tailed or two-tailed. The test statistic, which is the z-score calculated from the sample proportion, is then compared to the critical value. If the test statistic falls in the rejection region (beyond the critical value), the null hypothesis is rejected, indicating that the population proportion is significantly different from the hypothesized value.
• Analyze the role of the critical value in the context of confidence interval estimation for a single population mean using the Student's t-distribution (8.2).
  • In the context of 8.2 A Single Population Mean Using the Student's t-Distribution, the critical value is used to determine the boundaries of the confidence interval for the population mean. The critical value is obtained from the Student's t-distribution and is based on the chosen confidence level and the degrees of freedom. The critical value is then used to calculate the margin of error, which is added and subtracted from the sample mean to create the confidence interval. The critical value ensures that the confidence interval contains the true population mean with the specified level of confidence, allowing researchers to make inferences about the population parameter.

Related terms

Null Hypothesis:

The null hypothesis is a statement that there is no significant difference or relationship between the variables being tested.

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.

Significance Level:

The significance level is the probability threshold used to determine whether to reject the null hypothesis, typically set at 5% (0.05) or 1% (0.01).