Explain the procedure for testing a hypothesis using the P-value Approach. What is the criterion for judging whether to reject the null hypothesis?

Verified step by step guidance

1. Start by stating the null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_a\)). The null hypothesis usually represents the status quo or no effect, while the alternative represents what you want to test for.
2. Collect sample data and calculate the appropriate test statistic based on the hypothesis test type (e.g., z-test, t-test). The test statistic measures how far the sample data deviates from what is expected under \(H_0\).
3. Determine the P-value, which is the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value, assuming the null hypothesis is true. This involves finding the area under the probability distribution curve corresponding to the test statistic.
4. Compare the P-value to the chosen significance level (\(\alpha\)), which is the threshold probability for rejecting \(H_0\). Common values for \(\alpha\) are 0.05, 0.01, or 0.10.
5. If the P-value is less than or equal to \(\alpha\), reject the null hypothesis \(H_0\); this suggests that the observed data is unlikely under \(H_0\). If the P-value is greater than \(\alpha\), do not reject \(H_0\), indicating insufficient evidence against it.

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population parameter based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (H1), then using sample evidence to determine whether to reject H0.

P-value

The P-value is the probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis is true. It quantifies the strength of evidence against H0; smaller P-values indicate stronger evidence to reject H0.

Decision Criterion for Rejecting the Null Hypothesis

In the P-value approach, the null hypothesis is rejected if the P-value is less than or equal to the chosen significance level (α), typically 0.05. This means the observed data is unlikely under H0, justifying its rejection in favor of the alternative hypothesis.