Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN: 9780079039897
Author: Carter
Publisher: McGraw Hill
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**ANOVA Analysis for Comparing Assembly Methods**

To determine if there is a significant difference in the number of units assembled correctly among three different assembly methods, an industrial engineer conducted an experiment with 36 employees. Each method was used by 12 workers, and the number of correctly assembled units was recorded. The analysis of variance (ANOVA) procedure was applied to this data. Below is the detailed transcription and explanation of the analysis:

### Data and Instructions for ANOVA Table

| **Source of Variation** | **Sum of Squares** | **Degrees of Freedom** | **Mean Square** | **F** | **p-value** |
|--------------------------|----------------------|-----------------------------|-----------------|--------|-------------|
| Treatments                      |                                    |                                           |                       |          |                  |
| Error                                |                                    |                                           |                       |          |                  |
| Total                                  |                                    |                                           |                       |          |                  |

- SST (Total Sum of Squares) = 12,620
- SSTR (Sum of Squares due to Treatments) = 4,520

### Steps and Hypotheses

**(a) Setup of ANOVA Table**

Calculate the degrees of freedom for each source of variation:
- **Treatments (Between Groups)**: k - 1 (where k is the number of groups)
- **Error (Within Groups)**: N - k (where N is the total number of observations)
- **Total**: N - 1 (sum of the two above degrees of freedom)

Use the given formulas:
- **Mean Square**: MS = SS/df
- **F-ratio**: F = MST/MSE 

**(b) Hypothesis Testing**

Using **α = 0.05**, test for a significant difference in means among the three assembly methods.

**Hypotheses:**
- **Null Hypothesis (H0)**: μ1 = μ2 = μ3 (All means are equal)
- **Alternative Hypothesis (Ha)**: Not all means are equal

Since the hypotheses are about comparing three methods (μ1, μ2, μ3), the selected hypotheses are:
- **H0: μ1 = μ2 = μ3**
- **Ha: Not all the population means are equal**

**Conclusion Derivation**

Find the **test statistic** from the ANOVA table and compare it against the F-distribution critical value or directly assess the **p-value** against the significance level (
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Transcribed Image Text:**ANOVA Analysis for Comparing Assembly Methods** To determine if there is a significant difference in the number of units assembled correctly among three different assembly methods, an industrial engineer conducted an experiment with 36 employees. Each method was used by 12 workers, and the number of correctly assembled units was recorded. The analysis of variance (ANOVA) procedure was applied to this data. Below is the detailed transcription and explanation of the analysis: ### Data and Instructions for ANOVA Table | **Source of Variation** | **Sum of Squares** | **Degrees of Freedom** | **Mean Square** | **F** | **p-value** | |--------------------------|----------------------|-----------------------------|-----------------|--------|-------------| | Treatments | | | | | | | Error | | | | | | | Total | | | | | | - SST (Total Sum of Squares) = 12,620 - SSTR (Sum of Squares due to Treatments) = 4,520 ### Steps and Hypotheses **(a) Setup of ANOVA Table** Calculate the degrees of freedom for each source of variation: - **Treatments (Between Groups)**: k - 1 (where k is the number of groups) - **Error (Within Groups)**: N - k (where N is the total number of observations) - **Total**: N - 1 (sum of the two above degrees of freedom) Use the given formulas: - **Mean Square**: MS = SS/df - **F-ratio**: F = MST/MSE **(b) Hypothesis Testing** Using **α = 0.05**, test for a significant difference in means among the three assembly methods. **Hypotheses:** - **Null Hypothesis (H0)**: μ1 = μ2 = μ3 (All means are equal) - **Alternative Hypothesis (Ha)**: Not all means are equal Since the hypotheses are about comparing three methods (μ1, μ2, μ3), the selected hypotheses are: - **H0: μ1 = μ2 = μ3** - **Ha: Not all the population means are equal** **Conclusion Derivation** Find the **test statistic** from the ANOVA table and compare it against the F-distribution critical value or directly assess the **p-value** against the significance level (
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