Certainly! Here are some questions structured around hypothesis testing using null (H₀) and alternative (Hₐ) hypotheses. I've also indicated whether each question is right-tailed, left-tailed, or two-tailed. The answers will be provided at the bottom.
Question 1
Context: A manufacturer claims that their light bulbs last more than 1000 hours on average.
- H₀: μ ≤ 1000 (The mean life of the light bulbs is less than or equal to 1000 hours)
- Hₐ: μ > 1000 (The mean life of the light bulbs is greater than 1000 hours)
Decision: Based on a sample mean of 1015 hours and a p-value of 0.03. (Right-tailed test)
Question 2
Context: A school administrator believes that the average test score of students is less than 75.
- H₀: μ ≥ 75 (The mean test score is greater than or equal to 75)
- Hₐ: μ < 75 (The mean test score is less than 75)
Decision: Based on a sample mean of 72 and a p-value of 0.10. (Left-tailed test)
Question 3
Context: A researcher claims that the new drug has the same effect as the old drug.
- H₀: μ₁ = μ₂ (The mean effect of the new drug is equal to that of the old drug)
- Hₐ: μ₁ ≠ μ₂ (The mean effect of the new drug is not equal to that of the old drug)
Decision: Based on a sample means showing significant differences, with a p-value of 0.04. (Two-tailed test)
Question 4
Context: A company claims that their battery lasts at least 200 hours.
- H₀: μ < 200 (The mean battery life is less than 200 hours)
- Hₐ: μ ≥ 200 (The mean battery life is greater than or equal to 200 hours)
Decision: Based on a sample mean of 198 hours and a p-value of 0.15. (Right-tailed test)
Answers
- Question 1: Reject H₀ (because p-value < alpha, typically 0.05).
- Question 2: Fail to reject H₀ (because p-value > alpha).
- Question 3: Reject H₀ (because p-value < alpha).
- Question 4: Accept H₀ (Fail to reject H₀ because p-value > alpha).
You can decide your significance level (alpha) based on the context to determine the outcome.
1 answer