2. Defective parts produced by machine 1 and machine 2 using manual and automatic loading of parts is shown in the table: Machine Machine 1 (M1) Machine 2 (M2) A. Calculate M1. YM2. Y.ML. VAL., and y... Trial 1 Trial 2 a. Source Trial 1 Trial 2 B. Table gives the Sum of squares and degrees of freedom Machine Loading Analysis of Variance Table Machine * Loading Error Total Loading Type Manual Loading (ML) 30 35 18 24 b. C. For each variation source d. P values C. Which factors have significant effect of number of defectives? Fill the table with degrees of freedom for machine, loading, machine-loading interaction Calculate the F values DF SS 180.500 8.000 51.000 239.500 Auto Part loading (AL) 28 33 21 25 MS 180.500 8.000 12.750 F-Value P-Value

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**Transcription for Educational Website**

---

**Title: Analysis of Defective Parts Production**

**Section 1: Data Overview**

- **Problem Statement:**
  - Defective parts produced by machine 1 and machine 2 using manual and automatic loading of parts are shown in the table below.

- **Data Table:**

| Machine      | Loading Type       |          |          |
|--------------|--------------------|----------|----------|
|              | Manual Loading (ML)|          | Auto Loading (AL) |
|              | Trial 1            | Trial 2  | Trial 1  | Trial 2 |
| Machine 1 (M1)| 30                | 35       | 28       | 33     |
| Machine 2 (M2)| 18                | 24       | 21       | 25     |

**Section 2: Calculations Required**

A. Calculate the following averages:
   - \( \bar{Y}_{M1\cdot} \)
   - \( \bar{Y}_{M2\cdot} \)
   - \( \bar{Y}_{ML\cdot} \)
   - \( \bar{Y}_{AL\cdot} \)
   - \( \bar{Y}_{\cdot\cdot} \)

B. Use the provided Analysis of Variance (ANOVA) table:
   1. Fill in the degrees of freedom for machine, loading, and machine-loading interaction.
   2. Calculate the F values for each source of variation.
   3. Determine the p-values for each source.
   4. Analyze which factors significantly affect the number of defectives.

**Section 3: Analysis of Variance Table**

| Source          | DF  | SS     | MS     | F-Value | P-Value |
|-----------------|-----|--------|--------|---------|---------|
| Machine         |     | 180.500| 180.500|         |         |
| Loading         |     | 8.000  | 8.000  |         |         |
| Machine*Loading |     |        |        |         |         |
| Error           |     | 51.000 | 12.750 |         |         |
| Total           |     | 239.500|        |         |         |

**Section 4: Questions to Explore**

C. Which factors have a significant
Transcribed Image Text:**Transcription for Educational Website** --- **Title: Analysis of Defective Parts Production** **Section 1: Data Overview** - **Problem Statement:** - Defective parts produced by machine 1 and machine 2 using manual and automatic loading of parts are shown in the table below. - **Data Table:** | Machine | Loading Type | | | |--------------|--------------------|----------|----------| | | Manual Loading (ML)| | Auto Loading (AL) | | | Trial 1 | Trial 2 | Trial 1 | Trial 2 | | Machine 1 (M1)| 30 | 35 | 28 | 33 | | Machine 2 (M2)| 18 | 24 | 21 | 25 | **Section 2: Calculations Required** A. Calculate the following averages: - \( \bar{Y}_{M1\cdot} \) - \( \bar{Y}_{M2\cdot} \) - \( \bar{Y}_{ML\cdot} \) - \( \bar{Y}_{AL\cdot} \) - \( \bar{Y}_{\cdot\cdot} \) B. Use the provided Analysis of Variance (ANOVA) table: 1. Fill in the degrees of freedom for machine, loading, and machine-loading interaction. 2. Calculate the F values for each source of variation. 3. Determine the p-values for each source. 4. Analyze which factors significantly affect the number of defectives. **Section 3: Analysis of Variance Table** | Source | DF | SS | MS | F-Value | P-Value | |-----------------|-----|--------|--------|---------|---------| | Machine | | 180.500| 180.500| | | | Loading | | 8.000 | 8.000 | | | | Machine*Loading | | | | | | | Error | | 51.000 | 12.750 | | | | Total | | 239.500| | | | **Section 4: Questions to Explore** C. Which factors have a significant
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