Hypothesis testing is a fundamental aspect of statistical inference used by researchers to make decisions about population parameters based on sample data. It involves formulating a hypothesis, collecting data, and then using statistical methods to determine whether the evidence supports the hypothesis or not. Here’s a detailed explanation of the process:
Example Scenario
Research Question: Does a new drug reduce blood pressure more effectively than the current standard drug?
- Null Hypothesis (H₀): The new drug does not reduce blood pressure more effectively than the standard drug (( \mu_{\text{new}} = \mu_{\text{standard}} )).
- Alternative Hypothesis (H₁): The new drug reduces blood pressure more effectively than the standard drug (( \mu_{\text{new}} < \mu_{\text{standard}} )).
- Significance Level: α = 0.05.
- Data Collection: Random sample of patients, measuring blood pressure reduction.
- Test Selection: Conduct a t-test for independent samples.
- Calculate Test Statistic: Use sample data to calculate the t-value.
- Determine P-Value: Compare the t-value to the t-distribution to find the p-value.
- Decision and Conclusion: If p ≤ 0.05, reject H₀ and conclude that the new drug is more effective. If p > 0.05, do not reject H₀.
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