Three different methods for assembling a product were proposed by an Industrial engineer. To Investigate the number of units assembled correctly with each method, 36 employees were randomly selected and randomly assigned to the three proposed methods In such a way that each method was used by 12 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. The following results were obtained: SST = 12,750; SSTR = 4,510. (a) Set up the ANOVA table for this problem. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.) Source of Varlation Degrees of Freedom Mean Square Sum of Squares F p-value Treatments Error Total (b) Use a- 0.ós to test for any significant difference in the means for the three assembly methods. State the null and alternative hypotheses. O Ho: H H2 H O Ho: At least two of the population means are equal. H At least two of the population means are different. H Not all the population means are equal. O Ho: Not all the population means are equal. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value-
Three different methods for assembling a product were proposed by an Industrial engineer. To Investigate the number of units assembled correctly with each method, 36 employees were randomly selected and randomly assigned to the three proposed methods In such a way that each method was used by 12 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. The following results were obtained: SST = 12,750; SSTR = 4,510. (a) Set up the ANOVA table for this problem. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.) Source of Varlation Degrees of Freedom Mean Square Sum of Squares F p-value Treatments Error Total (b) Use a- 0.ós to test for any significant difference in the means for the three assembly methods. State the null and alternative hypotheses. O Ho: H H2 H O Ho: At least two of the population means are equal. H At least two of the population means are different. H Not all the population means are equal. O Ho: Not all the population means are equal. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value-
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text:**ANOVA Analysis for Assembly Method Comparison**
Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 36 employees were randomly selected and randomly assigned to the three proposed methods, in such a way that each method was used by 12 workers. The number of units assembled correctly was recorded, and an analysis of variance procedure was applied to the resulting data set. The following results were obtained: SST (Total Sum of Squares) = 12,750; SSTR (Sum of Squares for Treatments) = 4,510.
**Task:**
**(a) Set up the ANOVA table for this problem.**
*Round your values for Mean Square Error (MSE) and the F statistic to two decimal places, and the p-value to four decimal places.*
| Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | p-value |
|---------------------|----------------|--------------------|-------------|-----|---------|
| Treatments | | | | | |
| Error | | | | | |
| Total | | | | | |
**(b) Use α = 0.05 to test for any significant difference in the means for the three assembly methods.**
**State the null and alternative hypotheses:**
- \( H_0 \): \( \mu_1 = \mu_2 = \mu_3 \)
\( H_a \): At least two of the means are different.
- \( H_0 \): \( \mu_1 \neq \mu_2 = \mu_3 \)
\( H_a \): \( \mu_1 = \mu_2 \neq \mu_3 \)
- \( H_0 \): At least two of the population means are equal.
\( H_a \): At least two of the population means are different.
- \( H_0 \): \( \mu_1 = \mu_2 = \mu_3 \)
\( H_a \): Not all population means are equal.
- \( H_0 \): Not all the population means are equal.
\( H_a \): \( \mu_1 = \mu_2 = \mu_3 \)
**Calculate:**
1. **Test Statistic:**
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