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. 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.
Source of Variation Sum of Squares Degrees of Freedom Mean Square F
Treatments (Methods)
Error
Total
At the = 0.01 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?
ANOVA Completely Randomized Design
Batch Method A Method B Method C
1 164 141 124
2 142 158 122
3 167 127 134
4 144 141 141
5 149 137 153
6 170 148 130
Sample Size
Sum
Sample Mean
Sample Variance
Sample Standard
Deviation
Grand Mean
Group Count
Observation Count
Source of Variation Sum of Squares df Mean Square p-value
Treatments (Methods)
Error
Total 0.01
Level of significance
Reject nul
Are the means equal?