Question

Give me some questions with rejecting the null, accepting the null, and failure to reject null with H_0 and H_a (show the answers at the bottom) and incorporate >,<, more than equal, less than equal, equal or not, and =
(show if its right tailed, left tailed, or two tailed)

Answer 1

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
1. **Question 1:** Reject H₀ (because p-value < alpha, typically 0.05).
2. **Question 2:** Fail to reject H₀ (because p-value > alpha).
3. **Question 3:** Reject H₀ (because p-value < alpha).
4. **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.