MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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### Hypothesis Testing Example

The federal government is conducting a study to test a hypothesis concerning the average age of men and women filing for Social Security. The specific hypothesis states that the average age of men filing is smaller than the average age of women. To correctly test this hypothesis, we need to establish our null (H₀) and alternative (H₁) hypotheses.

**Hypotheses Options:**

1. **Option 1:**
   - \( H_0: \mu_{Men} = \mu_{Women} \)
   - \( H_1: \mu_{Men} \neq \mu_{Women} \)

2. **Option 2:**
   - None of these

3. **Option 3:**
   - \( H_0: \mu_{Men} = \mu_{Women} \)
   - \( H_1: \mu_{Men} > \mu_{Women} \)

4. **Option 4:**
   - \( H_0: \mu_{Men} = \mu_{Women} \)
   - \( H_1: \mu_{Men} < \mu_{Women} \)

The correct hypotheses for this study are:

- **Null Hypothesis (\( H_0 \))**:  
  The average age of men filing for Social Security is equal to the average age of women.  
  \( H_0: \mu_{Men} = \mu_{Women} \)

- **Alternative Hypothesis (\( H_1 \))**:  
  The average age of men filing for Social Security is smaller than the average age of women.  
  \( H_1: \mu_{Men} < \mu_{Women} \)

This is represented by Option 4, which is selected.

By establishing these hypotheses, the federal government can conduct appropriate statistical tests to determine if there is sufficient evidence to support the claim that the average age of men filing is indeed smaller than that of women.
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Transcribed Image Text:### Hypothesis Testing Example The federal government is conducting a study to test a hypothesis concerning the average age of men and women filing for Social Security. The specific hypothesis states that the average age of men filing is smaller than the average age of women. To correctly test this hypothesis, we need to establish our null (H₀) and alternative (H₁) hypotheses. **Hypotheses Options:** 1. **Option 1:** - \( H_0: \mu_{Men} = \mu_{Women} \) - \( H_1: \mu_{Men} \neq \mu_{Women} \) 2. **Option 2:** - None of these 3. **Option 3:** - \( H_0: \mu_{Men} = \mu_{Women} \) - \( H_1: \mu_{Men} > \mu_{Women} \) 4. **Option 4:** - \( H_0: \mu_{Men} = \mu_{Women} \) - \( H_1: \mu_{Men} < \mu_{Women} \) The correct hypotheses for this study are: - **Null Hypothesis (\( H_0 \))**: The average age of men filing for Social Security is equal to the average age of women. \( H_0: \mu_{Men} = \mu_{Women} \) - **Alternative Hypothesis (\( H_1 \))**: The average age of men filing for Social Security is smaller than the average age of women. \( H_1: \mu_{Men} < \mu_{Women} \) This is represented by Option 4, which is selected. By establishing these hypotheses, the federal government can conduct appropriate statistical tests to determine if there is sufficient evidence to support the claim that the average age of men filing is indeed smaller than that of women.
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