Overview Of The Research Department Of An Appliance M 797135

Overview the Research Department Of An Appliance Manufacturing Firm Has

The research department of an appliance manufacturing firm has developed a new bimetallic thermal sensor for its toaster. The new sensor aims to improve temperature sensing and reduce the number of toasters returned under the one-year warranty. The department claims that this new sensor will decrease appliance returns by between 2% and 6%. To verify this claim, the testing department tested a sample of toasters equipped with the new sensor and a sample with the old sensor, observing the number of returns after a year of use. Specifically, out of 250 toasters with the new sensor, 8 would have been returned, while out of 250 toasters with the old sensor, 17 would have been returned. As the manufacturing manager, the task is to apply a statistical procedure to evaluate whether the data support the research department’s claim.

Paper For Above instruction

Introduction

The effectiveness of technological innovations in manufacturing hinges significantly on empirical validation through statistical analysis. In the context of the appliance manufacturing firm's initiative to improve toaster designs via a new bimetallic thermal sensor, it is critical to determine whether the sensor genuinely reduces product returns under warranty. The research department posits that the new sensor will lower the return rate by approximately 2% to 6%. To substantiate or refute this claim, the testing department conducted a comparative analysis based on a sample of toasters with the new sensor and a control group with the old sensor, recording warranty returns after one year of consumer use. The core question is whether the observed reduction in return rates is statistically significant and consistent with the claimed improvement.

Problem Summary

The primary issue is to evaluate if the new sensor substantively decreases the warranty return rate for toasters compared to the old sensor. The initial data indicates that 8 out of 250 toasters with the new sensor would have been returned, versus 17 out of 250 with the old sensor. These figures suggest a potential reduction from 6.8% to 3.2%, but whether this difference is statistically significant needs to be tested. The company's objective is to validate the claim that the new sensor reduces return rates by at least 2%, ideally up to 6%, ensuring the investment in new technology is justified and economically beneficial.

Proposed Statistical Inference Method

The appropriate statistical approach for this analysis is hypothesis testing for the difference between two proportions. This method compares the observed return rates in the two samples to determine if the difference is statistically significant beyond what might occur by chance. Specifically, a two-proportion z-test is suitable because it evaluates whether the observed difference in return rates (0.032 vs. 0.068) is significant at a given confidence level, typically 95%. By employing this test, we can assess the null hypothesis that there is no difference in the return rates against the alternative hypothesis that the new sensor reduces returns by a specified margin.

Statistical Calculations and Flowchart Development

Using Excel, the following steps are undertaken to perform the analysis:

• Calculate the sample proportions:
  • p1 = 8/250 = 0.032 (new sensor)
  • p2 = 17/250 = 0.068 (old sensor)
• Determine the pooled proportion:

  p̂ = (8 + 17) / (250 + 250) = 25 / 500 = 0.05

• Compute the standard error (SE):

  SE = sqrt [p̂(1 - p̂) (1/n1 + 1/n2)] = sqrt [0.05 0.95 * (1/250 + 1/250)] ≈ 0.0195

• Calculate the z-statistic:

  z = (p1 - p2) / SE = (0.032 - 0.068) / 0.0195 ≈ -1.85

• Compare the z-value to critical value at α = 0.05 (two-tailed):

  Critical value ≈ ±1.96

Based on the calculations, since |z| ≈ 1.85

Flowchart creation in Excel involves these steps:

1. State hypotheses (null and alternative).

2. Collect sample data and compute sample proportions.

3. Calculate the pooled proportion.

4. Calculate the standard error.

5. Compute the z-test statistic.

6. Determine the critical value.

7. Make a decision: reject or fail to reject the null hypothesis.

8. Conclude whether the data support the research claim.

Conclusion

Based on the statistical analysis, there is insufficient evidence to conclusively support the research department's claim that the new bimetallic thermal sensor reduces toaster returns by 2% to 6%. The observed reduction from 6.8% to 3.2% in return rates is suggestive but not statistically significant at the 95% confidence level. It implies that while the new sensor might have a positive effect, further testing with larger samples or additional data may be necessary to confirm its efficacy. Making informed decisions about product improvements should rely on rigorous statistical validation to ensure investments yield tangible benefits.

References

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