Common Mistakes When Performing the Five Steps of Hypothesis Testing

📚 Quick Study Guide

• 🧪 Hypothesis Formulation: The null hypothesis ($H_0$) represents the status quo, while the alternative hypothesis ($H_1$ or $H_a$) represents the claim you're trying to prove.
• 📊 Setting the Significance Level ($\alpha$): Common values are 0.05 or 0.01. This determines the threshold for rejecting the null hypothesis.
• 📈 Calculating the Test Statistic: This depends on the type of test (e.g., t-test, z-test, chi-square test). The formula varies accordingly.
• ⚖️ Making a Decision: Compare the p-value to $\alpha$. If p-value $\leq \alpha$, reject $H_0$. Otherwise, fail to reject $H_0$.
• 📝 Drawing a Conclusion: State your findings in the context of the original research question. Avoid saying you've "proven" anything; instead, say there is "sufficient evidence" or "insufficient evidence".

Practice Quiz

1. Which of the following is a common mistake when formulating the null hypothesis?
   1. A. Failing to include an equality sign.
   2. B. Making the null hypothesis too specific.
   3. C. Always setting the significance level to 0.05.
   4. D. Using the alternative hypothesis as the null.
2. What's a frequent error when choosing a significance level ($\alpha$)?
   1. A. Always choosing $\alpha$ = 0.10.
   2. B. Selecting $\alpha$ based on the desired outcome.
   3. C. Forgetting to state the significance level.
   4. D. Ignoring the sample size when choosing $\alpha$.
3. A researcher calculates a p-value of 0.06 and sets $\alpha$ = 0.05. They reject the null hypothesis. What error did they make?
   1. A. Type I error.
   2. B. Type II error.
   3. C. No error, the null hypothesis should be rejected.
   4. D. Error in calculating the p-value.
4. Which of the following is a mistake when calculating the test statistic?
   1. A. Using the correct formula.
   2. B. Applying the wrong degrees of freedom.
   3. C. Checking assumptions of the test.
   4. D. Clearly stating the hypothesis.
5. What is a common error when making a decision based on the p-value?
   1. A. Correctly interpreting the p-value.
   2. B. Comparing the p-value to the test statistic.
   3. C. Failing to reject the null hypothesis when p-value > $\alpha$.
   4. D. Rejecting the null hypothesis when p-value > $\alpha$.
6. Which statement reflects a common mistake in drawing conclusions?
   1. A. Stating that the null hypothesis is "accepted".
   2. B. Acknowledging the limitations of the study.
   3. C. Stating findings in the context of the research question.
   4. D. Clearly stating the level of significance.
7. Why is it a mistake to ignore the assumptions of a statistical test?
   1. A. It always leads to a Type I error.
   2. B. The test results may be unreliable.
   3. C. It simplifies the analysis.
   4. D. It increases the power of the test.