Overview Of The Research Department Of An Appliance M 040519

Overviewthe Research Department Of An Appliance Manufacturing Firm Has

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 facing the appliance manufacturing firm centers on quantifying the effectiveness of a newly developed solid-state switch intended to reduce product returns under warranty. The research department asserts that this new switch can decrease the return rate by 3% to 6%. To evaluate this claim, the testing department conducted an experiment comparing return rates between blenders equipped with the new switch and those with the existing (old) switch, simulating a year’s worth of wear and tear.

The data collected reveals that out of 250 blenders with the new switch, 9 would have been returned, indicating a return rate of 3.6%. Conversely, the old switch model experienced 16 returns out of 250 units, translating to a return rate of 6.4%. These observed rates suggest that the new switch may indeed lead to a reduction in returns, consistent with the research department’s claim, but statistical analysis is necessary to determine whether this difference is statistically significant or due to random variation.

Statistical Inference Selection

To evaluate the claim, the appropriate statistical procedure is hypothesis testing for the difference between two proportions. This involves establishing a null hypothesis that posits no difference in return rates between the two switch types, versus an alternative hypothesis that the new switch leads to a lower return rate by at least 3% (or 6%).

The null hypothesis (H₀): p₁ - p₂ ≥ -0.03 (or equivalently, the new switch does not lower returns by more than 3%)

Alternative hypothesis (H₁): p₁ - p₂

Using a two-proportion z-test enables the assessment of whether the observed difference in return rates is statistically significant, supporting decision-making regarding the efficacy of the new switch.

Supporting Scholarly Reference

According to Ott and Longnecker (2015), hypothesis testing of two proportions is a common technique used in quality control and process improvement studies within manufacturing contexts. They emphasize the importance of choosing the correct level of significance and ensuring assumptions such as independence of samples and sufficient sample size are met.

Flowchart Development Using Excel

The flowchart in Excel will follow these steps:

1. Define hypotheses: null and alternative hypotheses.
2. Collect the sample data: return counts with each switch type.
3. Calculate sample proportions for each group.
4. Determine the pooled proportion.
5. Calculate the standard error of the difference between proportions.
6. Compute the z-statistic for the difference.
7. Determine the p-value associated with the z-statistic from standard normal distribution.
8. Compare p-value to significance level (α = 0.05) to accept or reject H₀.
9. Conclude whether the new switch significantly reduces returns.

The flowchart in Excel will graphically depict these sequential steps with decision blocks, calculation steps, and conclusions, providing clarity in the inference process.

Calculation of Statistical Measures

For the data:

• New switch: n₁=250, x₁=9, p̂₁=9/250=0.036
• Old switch: n₂=250, x₂=16, p̂₂=16/250=0.064

Pooled proportion (p̂):

p̂ = (x₁ + x₂) / (n₁ + n₂) = (9+16) / (250+250) = 25/500 = 0.05

Standard error (SE):

SE = √[p̂(1 - p̂)(1/n₁ + 1/n₂)] = √[0.050.95(1/250 + 1/250)] ≈ √[0.0475*(0.008)] ≈ √[0.00038] ≈ 0.0195

Z-statistic:

Z = (p̂₁ - p̂₂)/SE = (0.036 - 0.064)/0.0195 ≈ -0.028/0.0195 ≈ -1.44

From standard normal tables, the p-value for Z = -1.44 is approximately 0.075 (for a one-tailed test). Since 0.075 > 0.05, we fail to reject the null hypothesis at the 5% significance level, indicating insufficient evidence to conclusively support that the new switch reduces returns by at least 3%.

Conclusion

Based on the statistical analysis, while the observed data suggests that the new switch may lead to a reduction in returns, the evidence is not strong enough at the conventional 5% significance level to definitively confirm the research department’s claim. The difference, although in the expected direction, is not statistically significant, implying that further testing with larger samples or additional controls may be necessary to substantiate the claim. Nonetheless, the results are promising and suggest that the new switch has potential benefits that warrant further investigation and possibly broader implementation.

References

• Ott, R. L., & Longnecker, M. (2015). An Introduction to Statistical Methods and Data Analysis. Cengage Learning.
• Montgomery, D. C. (2019). Introduction to Statistical Quality Control. Wiley.
• Levine, D. M., Krehbiel, T. C., & Stephan, D. (2014). Statistics for Managers Using Microsoft Excel. Pearson.
• Walpole, R. E., Myers, R. H., Myers, S. L., & Ye, K. (2012). Probability & Statistics for Engineering and the Sciences. Pearson.
• Gerald, K. P., & Farlow, S. J. (2017). Statistics for Business and Economics. McGraw-Hill Education.
• Rumsey, D. J. (2016). Statistics For Dummies. Wiley.
• Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the Practice of Statistics. W. H. Freeman.
• Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences. Routledge Academic.
• Sheskin, D. J. (2011). Handbook of Parametric and Nonparametric Statistical Procedures. Chapman & Hall/CRC.
• Hogg, R. V., & Tanis, E. (2019). Probability and Statistical Inference. Pearson.