A manufacturing company has been selected to assemble a small but important component that will be used during the construction of numerous infrastructure projects. The company anticipates the need to assemble several million components over the next several years. Company engineers select three potential assembly methods: Method A, Method B, and Method C. Management would like to select the method that produces the fewest number parts per 10,000 parts produced that do not meet specifications. It may also be possible that there is no statistical difference between the three methods in which case the lowest cost method will be selected for production. While all parts are checked before leaving the factory, the best method will reduce the number of parts that need to be recycled back into the production process.To test each method, six batches of 10,000 components are produced using each of the three methods. The number of components out of specification are recorded in the Microsoft Excel Online file below. Analyze the data to determine if there is any difference in the mean number of components that are out of specificaion among the three methods. After conducting the analysis report the findings to the management team. ### Analysis of Variance (ANOVA) Problem SetThis exercise is designed to guide you through the process of setting up and solving an ANOVA table. Follow the instructions carefully, and round your answers as specified.#### Questions:**a. Compute the sum of squares between treatments (assembly methods).**\[ \_\_\_\_\_\_ \]**b. Compute the mean square between treatments (to 1 decimal if necessary).**\[ \_\_\_\_\_\_ \]**c. Compute the sum of squares due to error.**\[ \_\_\_\_\_\_ \]**d. Compute the mean square due to error (to 1 decimal if necessary).**\[ \_\_\_\_\_\_ \]**e. Set up the ANOVA table for this problem. Round all sum of squares to the nearest whole number. Round all Mean Squares to one decimal place. Round \( F \) to two decimal places.**##### ANOVA Table:| **Source of Variation** | **Sum of Squares** | **Degrees of Freedom** | **Mean Square** | **\( F \)** ||---------------------------|--------------------|------------------------|-----------------|-------------|| Treatments (Methods) | | | | || Error | | | | || Total | | | | |**f. At the \(\alpha = 0.05\) level of significance, test whether the means for the three methods are equal.** **Calculate the value of the test statistic (to 2 decimals):** \[ \_\_\_\_\_\_ \] **The \(p\)-value is (to 4 decimals):** \[ \_\_\_\_\_\_ \] **What is your conclusion for management?** \[ \_\_\_\_\_\_ \]Make sure to transfer the computations on your worksheet accurately to arrive at the correct conclusion. This exercise aims to enhance your skills in performing ANOVA tests and interpreting their results. ### Educational Resource: Understanding ANOVA (Analysis of Variance)#### **Introduction to ANOVA Completely Randomized Design**This resource provides a detailed overview of how to perform a one-way ANOVA (Analysis of Variance) with a completely randomized design using a sample dataset. One-way ANOVA allows you to determine whether there are any statistically significant differences between the means of three or more independent groups.#### **Sample Data Overview**The dataset in this example consists of six batches, which have been tested using three different methods (Method A, Method B, and Method C). The responses recorded for each batch under each method are as follows:| Batch | Method A | Method B | Method C ||-------|----------|----------|----------|| 1 | 163 | 147 | 125 || 2 | 141 | 157 | 122 || 3 | 168 | 129 | 135 || 4 | 135 | 145 | 145 || 5 | 149 | 137 | 152 || 6 | 172 | 141 | 125 |#### **Statistical Metrics Calculation**1. **Sample Size**: Number of observations per method.2. **Sum**: Total sum of observations per method.3. **Sample Mean**: Average of observations per method.4. **Sample Variance**: Measure of how data points differ from the mean.5. **Sample Standard Deviation**: Square root of the variance.#### **Formulas and Outputs**The following fields include their respective formulas and are auto-calculated:- **Sample Size**- **Sum**- **Sample Mean**- **Sample Variance**- **Sample Standard Deviation**- **Grand Mean**: Overall average of all observations.- **Group Count**: Number of methods.- **Observation Count**: Total number of observations.#### **Source of Variation Calculation**1. **Treatments (Methods)**: - **Sum of Squares (SS)**: Measures the variability between group means. - **Degrees of Freedom (df)**: Number of groups minus one. - **Mean Square (MS)**: Sum of squares divided by degrees of freedom. - **F-value**: Ratio of mean square between the treatments and the error. - **p-value

For completely randomized design, the dataset is given as-Method AMethod BMethod…

Answered: A manufacturing company has been…

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P