20) Do a hypothesis for the following, make sure to include and label all five steps: Test the claim the samples come from populations with the same mean. Use a .05 significance level. Source DF SS MS 4.5 Factor 13.5 5.17 0.011 Error 16 13.925 27.425 0.87 Total 19

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### Hypothesis Testing Example

**Problem:** 

20) Perform a hypothesis test for the following scenario, making sure to include and label all five steps. Test the claim that the samples come from populations with the same mean. Use a 0.05 significance level.

**Data Provided:**

| Source | DF | SS   | MS  | F    | p    |
|--------|----|------|-----|------|------|
| Factor | 3  | 13.5 | 4.5 | 5.17 | 0.011|
| Error  | 16 | 13.925| 0.87|      |      |
| Total  | 19 | 27.425|     |      |      |

**Explanation of Terms and table:**

- **Source:** Refers to the factors (treatments) and error in the analysis.
- **DF (Degrees of Freedom):** The number of values in the final calculation of a statistic that are free to vary.
- **SS (Sum of Squares):** The sum of the squared deviations from the mean.
- **MS (Mean Square):** The sum of squares divided by their respective degrees of freedom.
- **F:** The F-statistic calculated for the hypothesis test.
- **p:** The p-value associated with the F-statistic.

**Steps for Hypothesis Testing:**

1. **State the Hypotheses:**
   - **Null Hypothesis (H₀):** The population means are equal (μ₁ = μ₂ = μ₃ = μ₄).
   - **Alternative Hypothesis (H₁):** At least one population mean is different from the others.

2. **Set the Significance Level:**
   - The significance level (α) is 0.05.

3. **Calculate the Test Statistic:**
   - The given F-statistic is 5.17.

4. **Determine the p-value:**
   - The p-value given is 0.011.

5. **Make a Decision:**
   - If the p-value (0.011) is less than the significance level (0.05), we reject the null hypothesis H₀.

**Conclusion:**
Since the p-value (0.011) is less than the significance level (0.05), we reject the null hypothesis. This indicates that there is sufficient evidence to conclude that at least one of
Transcribed Image Text:### Hypothesis Testing Example **Problem:** 20) Perform a hypothesis test for the following scenario, making sure to include and label all five steps. Test the claim that the samples come from populations with the same mean. Use a 0.05 significance level. **Data Provided:** | Source | DF | SS | MS | F | p | |--------|----|------|-----|------|------| | Factor | 3 | 13.5 | 4.5 | 5.17 | 0.011| | Error | 16 | 13.925| 0.87| | | | Total | 19 | 27.425| | | | **Explanation of Terms and table:** - **Source:** Refers to the factors (treatments) and error in the analysis. - **DF (Degrees of Freedom):** The number of values in the final calculation of a statistic that are free to vary. - **SS (Sum of Squares):** The sum of the squared deviations from the mean. - **MS (Mean Square):** The sum of squares divided by their respective degrees of freedom. - **F:** The F-statistic calculated for the hypothesis test. - **p:** The p-value associated with the F-statistic. **Steps for Hypothesis Testing:** 1. **State the Hypotheses:** - **Null Hypothesis (H₀):** The population means are equal (μ₁ = μ₂ = μ₃ = μ₄). - **Alternative Hypothesis (H₁):** At least one population mean is different from the others. 2. **Set the Significance Level:** - The significance level (α) is 0.05. 3. **Calculate the Test Statistic:** - The given F-statistic is 5.17. 4. **Determine the p-value:** - The p-value given is 0.011. 5. **Make a Decision:** - If the p-value (0.011) is less than the significance level (0.05), we reject the null hypothesis H₀. **Conclusion:** Since the p-value (0.011) is less than the significance level (0.05), we reject the null hypothesis. This indicates that there is sufficient evidence to conclude that at least one of
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