DAT 475 Project two

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Southern New Hampshire University *

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Statistics

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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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