A two-tailed test is conducted at the 5% significance level. What is the P-value required to reject the null hypothesis?

For a two-tailed test at the 5% significance level:

If test statistic is in the top 2.5% or bottom 2.5%, it is considered statistically significant. (In a two-tailed test, you divide the significance level by 2).

To determine the p-value required to reject the null hypothesis in a two-tailed test at the 5% significance level, you need to compare the p-value obtained from the test to the significance level.

In a two-tailed test, the null hypothesis assumes no difference or association between variables, while the alternative hypothesis assumes a difference or association in both directions.

To calculate the p-value, you would typically use a statistical test, such as a t-test or z-test, depending on the context. These tests generate a test statistic, which is then compared to a reference distribution to obtain a p-value.

If the obtained p-value is less than or equal to the significance level (in this case, 5%), you would reject the null hypothesis. Conversely, if the p-value is greater than the significance level, you would fail to reject the null hypothesis.

Therefore, the p-value required to reject the null hypothesis in a two-tailed test at the 5% significance level is any p-value that is less than or equal to 0.05.

In a two-tailed test conducted at the 5% significance level, the P-value required to reject the null hypothesis is less than or equal to 0.025 for each tail. This is because the 5% significance level is split evenly between the two tails (2.5% in each tail).