DAT 475 Project two

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Feb 20, 2024

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Southern New Hampshire University DAT 475 Applied Data Analysis Project Two Case Study February 11, 2024

Hypothesis Test Procedure In Project One, we examined the defects in a manufacturing company in Tijuana, Mexico. They manufactured electronic boards and had seen an increase in demand for their product. They also saw an increase in the defects of the electronic boards and the Thru-Holes components. Based on this information and working with the management team, we will conduct a one-way Analysis of Variance, or ANOVA testing to evaluate and examine the proposed outcomes to improve the welding and soldering process at the company. After reviewing the data set provided, we determined that we would utilize µ 1, µ2, and µ3 along with a Variance, σ 2, to parameterize the model. Developing Hypothesis Statements For this analysis, our goal is to consider the outputs of the three production lines and determine if there is a statistically significant difference between the number of defects, measured by the overall percentage of defects compared to products with no defects (Bevans, 2023). If the test results indicate that there is a significantly higher percentage of defects from one or more production lines versus the others, the company can correct the defective production lines based off of these results. In order to figure out this information, we will create and test hypotheses from the sample mean data provided using the one-way ANOVA method. The hypothesis statements are: The null and alternate hypothesis are below, where significance level is α = 0.05 H 0 = µ1 = µ2 = µ3 meaning there is no significant difference between the three means

H 1 = µ1 ≠ µ2 ≠ µ3 meaning there is at least one significant difference between the three means The defective model groups in percentage metrics are shown in Figure 1 below. Model1 Model2 Model3 30 6.67 7.23 14 3.11 3.37 11.5 2.56 2.77 8 1.78 1.93 5 1.11 1.2 Figure 1: Defect Dataset Percentages Performing Hypothesis Testing Considering our hypothesis statements as stated below, we can conduct the one-way ANOVA test to analyze the data. H 0 = µ1 = µ2 = µ3 meaning there is no significant difference between the three means H 1 = µ1 ≠ µ2 ≠ µ3 meaning there is at least one significant difference between the three means Percentage N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum Model1 5 13.7 9.73139 4.35201 1.6169 25.7831 5 30 Model2 5 3.046 2.16359 0.96759 0.3595 5.7325 1.11 6.67 Model3 5 3.3 2.34615 1.04923 0.3869 6.2131 1.2 7.23 Total 15 6.68 7.5076 1.93845 2.5244 10.8396 1.11 30 Descriptives 95% Confidence Interval for Mean Percentage Sum of Squares df Mean Square F Sig. Between Groups 369.6 2 184.78 5.285 0.023 Within Groups 419.5 12 34.96 Total 789.1 14 ANOVA Figure 2: ANOVA Hypothesis Test

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Post-hoc testing and multiple comparisons between models noting the means for groups in homogenous subsets are shown below in Figure 3. Post Hoc Tests Dependent Variable: Percentage Tukey HSD (I) Group (J) Group Mean Difference (I-J) Std. Error Sig. Lower Bound Upper Bound Model 1 Model 2 10.654* 3.74 0.036 0.677 20.631 Model 3 10.400* 3.74 0.041 0.423 20.377 Model 2 Model 1 -10.654* 3.74 0.036 -20.631 -0.677 Model 3 -0.254 3.74 0.997 -10.231 9.723 Model 3 Model 1 -10.400* 3.74 0.041 -20.377 -4.232 Model 2 0.254 3.74 0.997 -9.723 10.231 * The mean difference is significant at the 0.05 level. Homogeneous Subsets Tukey HSD a Group N 1 2 Model 2 5 3.046 Model 3 5 3.3 Model 1 5 13.7 Sig. 0.997 1 Means for groups in homogeneous subsets are displayedt. a. Uses Harmonic Mean Sample Size = 5 95% Condfidence Interval Multiple Comparisons Percentage Subset for alpha = 0.05 Figure 3: Post Hoc Tests Interpreting Hypothesis Results

The ANOVA test results in Figure 2 and presents the Between, Within and Total group scores for Sum of Squares, degrees of freedom, and Mean Square. The F-statistic equals 5.285 and the P-value is .023. Knowing that the alpha value = 0.05, the P-value .023 is less than the significance level, we can reject the null hypothesis. By rejecting the null hypothesis, we determine that there is a significant difference between the means of the three models/production lines. The Post Hoc tests in Figure 3 are conducted when there is a significant difference in the ANOVA. The Multiple Comparisons table compares the models and provide a further investigation into the variations between the models. We can see that there is a significant difference between Model 1 and Model 2 as well as Model 1 and Model 3 with the P-value being less than .05. This allows us to reject the null hypothesis. In Model 2 and Model 3, we can see that there is not a significant difference between the models. Therefore, we would not reject the null hypothesis. Further reviewing the means of the models, the Homogeneous Subset in Figure 3 shows that the mean for Model 1 is significantly higher than the means of Model 2 and Model 3. It is also noted that Model 2 and Model 3 are closer in means and are in the same column (column 1). The ANOVA results show that we will reject the null hypothesis which stated that there was not a significant difference between the means of the models/production lines. The Post Hoc tests further show that the mean percentage of defects is significantly higher in Model 1. We can conclude that the model with the highest percentage of defects is Model 1, and this is where the stakeholders should begin their investigation into how to improve the defects from this production line.

References Bevans, R. (2023, June 22). ANOVA in R|A Complete Step-by-Step Guide with Examples . Scribbr. ANOVA in R | A Complete Step-by-Step Guide with Examples (scribbr.com) SNHU (2024). Project Case Study. SNHU. DAT 475 Project Case Study.pdf (snhu.edu)

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