Overview Of The Research Department Of An Appliance M 371265

Overview the Research Department Of An Appliance Manufacturing Firm Has

Overview the research department of an appliance manufacturing firm has developed a solid-state switch for its blender that the research department claims will reduce appliance returns under the one-year full warranty by 3%–6%. To determine if the claim can be supported, the testing department selects a group of the blenders manufactured with the new switch and a group with the old switch and subjects them to a normal year’s worth of wear. Out of 250 blenders tested with the new switch, nine would have been returned. Sixteen would have been returned out of the 250 blenders with the old switch. As the manager of the appliance manufacturing process, use a statistical procedure to verify or refute the research department’s claim.

Paper For Above instruction

The problem faced by the appliance manufacturing firm centers around the effectiveness of a new solid-state switch designed to reduce appliance returns within the warranty period. The research department claims that this new switch can decrease return rates by approximately 3% to 6%. To evaluate this assertion, the testing department conducted an experiment involving two groups of blenders—those equipped with the new switch and those with the existing switch—and measured the number of units that would have been returned after a year of use. The core objective is to statistically determine whether the observed differences in return rates support the research department’s claim.

Specifically, 250 blenders with the new switch resulted in nine potential returns, while 250 blenders with the old switch had sixteen potential returns. These figures translate into observed return rates of 3.6% (9/250) for the new switch and 6.4% (16/250) for the old switch. This difference suggests that the new switch may indeed be more effective; however, a formal statistical analysis is necessary to determine if this difference is statistically significant and attributable to the switch rather than random variation.

Proposed Statistical Inference Method

The appropriate statistical procedure to evaluate this situation is hypothesis testing for the difference between two population proportions. This involves comparing the return rates of the two groups — those with the new switch and those with the old switch — to determine whether the observed difference is statistically significant. The hypothesis test would use a z-test for the difference between proportions, which is appropriate given the large sample sizes (n=250 for each group).

The null hypothesis (H₀) asserts that there is no difference in return rates between blenders with the new switch and those with the old switch (p₁ = p₂). The alternative hypothesis (H₁) posits that the new switch leads to a lower return rate (p₁

Supporting Scholarly Reference

The choice of hypothesis testing for proportions is well-documented in statistical literature. For example, Howell (2012) emphasizes that z-tests for proportions are appropriate for comparing two independent samples, especially when sample sizes are sufficiently large to justify the normal approximation. This method is widely used in quality control and manufacturing process evaluation to determine the effectiveness of process changes (Montgomery, 2019). Therefore, the proposed hypothesis test aligns with established statistical practices for assessing improvements in product reliability.

Flowchart Development Using Excel

The proposed flowchart in Excel will outline the following steps: defining hypotheses, calculating the pooled proportion, calculating the standard error, computing the z-test statistic, determining the p-value, and making a decision to accept or reject the null hypothesis based on the significance level (e.g., α=0.05). This flowchart visualizes the process ensuring clarity and accuracy in executing the hypothesis test, essential for validating the research department’s claim.

Statistical Calculations and Decision

Based on the observed data, the return proportions are p̂₁ = 9/250 = 0.036 for the new switch and p̂₂= 16/250= 0.064 for the old switch. The pooled proportion (p̂) is calculated as:

p̂ = (9 + 16) / (250 + 250) = 25/500 = 0.05

The standard error (SE) for the difference between two proportions is:

SE = √[p̂(1 - p̂)(1/n₁ + 1/n₂)]

SE = √[0.05(0.95)(1/250 + 1/250)] ≈ 0.0195

The z-statistic is then:

z = (p̂₁ - p̂₂) / SE = (0.036 - 0.064) / 0.0195 ≈ -1.59

The critical z-value for a one-tailed test at α=0.05 is approximately -1.645. Since -1.59 > -1.645, the result is not statistically significant at the 5% level. Alternatively, the p-value associated with z = -1.59 is about 0.056, which slightly exceeds 0.05, indicating insufficient evidence to reject the null hypothesis at the 5% significance level.

This statistical outcome suggests that while the observed data show a lower return rate with the new switch, the evidence isn’t strong enough to conclusively prove the switch's effectiveness at the conventional 5% level. However, it is close, and with a larger sample size, the results might become statistically significant.

Conclusion

By applying hypothesis testing for proportions, the analysis indicates that the reduction in return rate from 6.4% to 3.6% is not statistically significant at the 5% level, although it suggests a promising improvement. Therefore, the manufacturing manager can cautiously conclude that the new solid-state switch potentially reduces returns in line with the research department’s claim, but further testing with larger samples or additional data may be necessary for more definitive validation.

References

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• Montgomery, D. C. (2019). Introduction to statistical quality control (8th ed.). Wiley.
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• Hogg, R. V., McKean, J., & Craig, A. T. (2019). Introduction to mathematical statistics (8th ed.). Pearson.
• Lewis, C. (2016). Quality control in manufacturing: Making data-driven decisions. Manufacturing Journal, 28(3), 45-52.
• Ross, S. M. (2014). Introduction to probability models (11th ed.). Academic Press.
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