Practical Applications of Hypothesis Testing: Case Studies for Statistics Students

📚 Quick Study Guide

• 🤔 Definition: Hypothesis testing is a statistical method used to make inferences about a population based on sample data.
• 📊 Null Hypothesis ($H_0$): A statement of no effect or no difference. We aim to disprove this.
• 🧪 Alternative Hypothesis ($H_1$): A statement that contradicts the null hypothesis. This is what we're trying to prove.
• 📈 P-value: The probability of observing a test statistic as extreme as, or more extreme than, the result obtained, assuming that the null hypothesis is true.
• ✔️ Significance Level ($\alpha$): A pre-determined threshold (usually 0.05) used to decide whether to reject the null hypothesis. If p-value $\leq \alpha$, we reject $H_0$.
• 📐 Common Tests: t-tests, z-tests, chi-square tests, ANOVA. The choice depends on the type of data and research question.
• 💡 Type I Error: Rejecting the null hypothesis when it is true (false positive).
• ⛔ Type II Error: Failing to reject the null hypothesis when it is false (false negative).

Practice Quiz

1. Question 1: A company wants to test if a new drug reduces blood pressure. The null hypothesis is that the drug has no effect. What is the alternative hypothesis?
   1. A) The drug increases blood pressure.
   2. B) The drug has no effect on blood pressure.
   3. C) The drug decreases blood pressure.
   4. D) The drug has some effect on blood pressure.
2. Question 2: In a hypothesis test, the p-value is 0.03, and the significance level ($\alpha$) is 0.05. What is the correct conclusion?
   1. A) Fail to reject the null hypothesis.
   2. B) Reject the null hypothesis.
   3. C) Accept the null hypothesis.
   4. D) The test is inconclusive.
3. Question 3: A researcher wants to determine if there is a relationship between smoking and lung cancer. Which statistical test is most appropriate?
   1. A) t-test
   2. B) ANOVA
   3. C) Chi-square test
   4. D) Regression analysis
4. Question 4: What does a Type I error represent in hypothesis testing?
   1. A) Failing to reject a false null hypothesis.
   2. B) Rejecting a true null hypothesis.
   3. C) Correctly rejecting a false null hypothesis.
   4. D) Correctly failing to reject a true null hypothesis.
5. Question 5: A factory claims that the average weight of their product is 500g. You suspect it's less. What is the appropriate null hypothesis ($H_0$)?
   1. A) $H_0: \mu < 500$
   2. B) $H_0: \mu > 500$
   3. C) $H_0: \mu = 500$
   4. D) $H_0: \mu \neq 500$
6. Question 6: You conduct a t-test to compare the means of two groups and obtain a p-value of 0.10. If your significance level is 0.05, what do you conclude?
   1. A) Reject the null hypothesis.
   2. B) Fail to reject the null hypothesis.
   3. C) Accept the alternative hypothesis.
   4. D) The test is statistically significant.
7. Question 7: Which of the following is NOT a step in hypothesis testing?
   1. A) State the null and alternative hypotheses.
   2. B) Calculate the test statistic.
   3. C) Accept the null hypothesis without calculating the p-value.
   4. D) Make a decision based on the p-value and significance level.