Research Department Of An Appliance Manufacturing Firm

The Research Department Of An Appliance Manufacturing Firm Has Develop

The research department of an appliance manufacturing firm has developed a new bimetallic thermal sensor for its toaster. The new sensor is claimed to reduce the number of toasters returned under the one-year full warranty by 2% to 6%. To verify this claim, the testing department sampled a group of toasters with the new sensor and a group with the old sensor, subjected them to a year’s wear, and recorded the number of returns. Specifically, out of 250 toasters with the new sensor, 8 would have been returned, and out of 250 toasters with the old sensor, 17 would have been returned. As the manager, you must evaluate whether the data supports the research department’s claim using an appropriate statistical inference method.

Paper For Above instruction

The problem presented by the appliance manufacturing firm pertains to evaluating the efficacy of a newly developed bimetallic thermal sensor integrated into their toasters. The core concern is whether this new sensor effectively reduces the incidence of product returns under the one-year warranty, as claimed by the research department. Returns are a critical metric for manufacturers, representing both customer satisfaction and financial implications. If the new sensor can statistically demonstrate a meaningful reduction in return rates, the firm can justify its investment and potentially gain a competitive advantage through improved product reliability.

To address this problem, an appropriate statistical inference technique must be identified. Given that the data involves comparing two proportions—namely, the proportion of toasters returned with the new sensor versus the proportion with the old sensor—a two-proportion z-test is suitable. This test evaluates whether the difference between two population proportions is statistically significant, thereby supporting or refuting the hypothesis that the new sensor reduces returns.

The null hypothesis (H₀) in this scenario states that there is no difference between the return rates of the two groups (i.e., the new sensor does not reduce returns). The alternative hypothesis (H₁) posits that the return rate with the new sensor is lower than that with the old sensor, implying a reduction in returns due to the new technology. Conducting a two-proportion z-test involves calculating the two sample proportions, their combined proportion, standard error, and the z-statistic, with the resulting p-value determining the statistical significance.

Using Excel, the steps are as follows: First, calculate the sample proportions: p₁ = 8/250 = 0.032 for the new sensor and p₂ = 17/250 = 0.068 for the old sensor. Next, compute the pooled proportion: p̂ = (8 + 17) / (250 + 250) = 25 / 500 = 0.05. Then, determine the standard error: SE = √[p̂(1 - p̂)(1/n₁ + 1/n₂)] and calculate the z-value: z = (p₁ - p₂) / SE. Using Excel's functions, these calculations can be automated.

The resulting p-value will inform whether the observed difference is statistically significant at a chosen significance level (e.g., α = 0.05). If the p-value is less than α, we reject the null hypothesis, supporting the research claim that the new sensor reduces returns by at least 2%. Conversely, if the p-value exceeds α, the data does not provide sufficient evidence to support the claimed reduction.

Constructing a flowchart in Excel involves outlining these steps: formulating hypotheses, calculating sample proportions, computing pooled proportion, standard error, z-score, and p-value, and finally, decision-making based on the p-value. Such a flowchart visualizes the logical sequence and statistical procedures involved.

Based on the calculations and significance testing, if the p-value indicates a statistically significant difference favoring the new sensor, the firm can confidently verify the research department's claim. If not, the claim cannot be supported by the evidence. This rigorous statistical approach ensures informed decision-making grounded in empirical data, aligning with best practices in manufacturing quality control.

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