A consumer analyst reports that the mean life of a certain type of alkaline battery is more than 63 months. Write the null and alternative hypotheses.

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Group of answer choices

Ho: μ = 63, Ha: μ < 63

Ho: μ = 63, Ha: μ > 63

Ho: μ = 63, Ha: μ ≥ 63

Ho: μ > 63, Ha: μ = 63

When writing null and alternative hypotheses, it's essential to understand the claim being made and how to structure the hypotheses accordingly.

### **Scenario:**
A consumer analyst claims that the mean life of a certain type of alkaline battery is **more than 63 months**.

### **Step 1: Identify the Claim**
- The claim is that the mean life of the battery is **more than 63 months**. This is the **alternative hypothesis** because it suggests a deviation from the status quo.

### **Step 2: Write the Hypotheses**
- **Null Hypothesis (\(H_0\))**: The null hypothesis represents the status quo or the default position. It is typically a statement of no effect or no difference. Here, it would state that the mean life of the battery is **63 months**.
  \[
  H_0: \mu = 63
  \]

- **Alternative Hypothesis (\(H_A\))**: The alternative hypothesis represents the claim being tested. It suggests that the mean life is **more than 63 months**.
  \[
  H_A: \mu > 63
  \]

### **Correct Answer:**
- **\( H_0: \mu = 63 \), \( H_A: \mu > 63 \)**

This matches the second option provided:

- **Ho: μ = 63, Ha: μ > 63**

### Do you need more details or have any other questions?

### Relative Questions:
1. What is the significance of the null hypothesis in hypothesis testing?
2. How do you decide between a one-tailed and a two-tailed test?
3. Why is the alternative hypothesis important in hypothesis testing?
4. Can the null hypothesis ever be accepted?
5. What does it mean to reject the null hypothesis?

### Tip:
Always align the alternative hypothesis with the direction of the claim, especially when determining if the test is one-tailed or two-tailed.

Understand null and alternative hypotheses in consumer analysis regarding the mean life of alkaline batteries. Learn how to formulate hypotheses and their significance in statistical testing.

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