A two-tailed test is conducted at the 5% significance level. What is the P-value required to reject the null hypothesis?
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To answer this question, we need to understand what a P-value is and how it relates to hypothesis testing.
In hypothesis testing, we start with a null hypothesis (H0) and an alternative hypothesis (Ha). The null hypothesis assumes that there is no significant difference or relationship between variables, while the alternative hypothesis assumes that there is a significant difference or relationship.
The P-value represents the probability of observing a test statistic (or a more extreme one) if the null hypothesis is true. It measures the strength of evidence against the null hypothesis. In other words, it tells us how likely we would see the observed data if the null hypothesis were true.
In a two-tailed test, we are testing for a difference in both directions. Let's say we have a null hypothesis that the mean is equal to a specific value (H0: μ = μ0), and the alternative hypothesis is that the mean is not equal to that specific value (Ha: μ ≠ μ0).
When conducting the test at a specific significance level, like 5%, we set a threshold for the P-value. If the P-value is less than or equal to this threshold, we reject the null hypothesis in favor of the alternative hypothesis.
In this case, with a two-tailed test conducted at the 5% significance level, we split the significance level (α) between the two tails of the distribution. This means that each tail will have an alpha level of 2.5% (0.025). Therefore, the P-value required to reject the null hypothesis would be less than or equal to 0.025.
If the computed P-value is less than or equal to 0.025, we reject the null hypothesis because the evidence suggests a significant difference. If the computed P-value is greater than 0.025, we fail to reject the null hypothesis because the evidence does not provide enough support for a significant difference.
It's important to note that the specific P-value required to reject the null hypothesis may vary depending on the statistical test or procedure being used. Nonetheless, in a two-tailed test conducted at a 5% significance level, the P-value required to reject the null hypothesis is less than or equal to 0.025.