The research department of an appliance manufacturing firm has developed a new bimetallic thermal sensor for its toaster.

Sample Solution

Presentation to the Director of the Manufacturing Plant

Slide 1: Title Slide

Title: Statistical Analysis of New Bimetallic Thermal Sensor for Toasters

Presenter: [Your Name]

Date: 2023-11-20

Slide 2: Problem Summary

The research department of an appliance manufacturing firm has developed a new bimetallic thermal sensor for its toaster. They claim that the new sensor will reduce appliance returns under the one-year full warranty by 2%-6%. To evaluate this claim, the testing department conducted a study comparing toasters with the new sensor to those with the old sensor.

Full Answer Section

Slide 3: Statistical Inference Proposal

To determine whether the new bimetallic thermal sensor reduces appliance returns, we will use a two-proportion z-test. This test is appropriate because we have two independent groups (toasters with new and old sensors) and we are comparing the proportions of defectives in each group.

Slide 4: Flowchart

1. State the null and alternative hypotheses.

Hâ‚€: The proportion of defective toasters with the new sensor is equal to the proportion of defective toasters with the old sensor.

H₁: The proportion of defective toasters with the new sensor is less than the proportion of defective toasters with the old sensor.

2. Calculate the sample proportions and standard error.

Sample proportion of defective toasters with new sensor = 8/250 = 0.032

Sample proportion of defective toasters with old sensor = 17/250 = 0.068

Standard error = √[(0.032)(0.968) / 250 + (0.068)(0.932) / 250] = 0.016

3. Compute the z-statistic.

z = (0.032 - 0.068) / 0.016 = -2.25

4. Determine the p-value.

Using a two-tailed z-test with α = 0.05, we find a p-value of approximately 0.012.

5. Make a decision.

Since the p-value is less than α, we reject the null hypothesis and conclude that there is significant evidence to suggest that the new bimetallic thermal sensor reduces appliance returns under the one-year full warranty.

Slide 5: Statistical Calculations

See Slide 4 for the statistical calculations.

Slide 6: Conclusion

The research department's claim that the new bimetallic thermal sensor will reduce appliance returns under the one-year full warranty by 2%-6% is supported by the statistical analysis.

Slide 7: Sources

[List of references]

Slide 8: Additional Considerations

While the statistical analysis provides evidence to support the research department's claim, it is important to note that this study was based on a limited sample size. Further testing with larger sample sizes would provide more definitive results.

Slide 9: Recommendations

Based on the results of this study, I recommend that the company consider implementing the new bimetallic thermal sensor in its toasters. This change could lead to a reduction in appliance returns and improve customer satisfaction.

Slide 10: Thank You

Thank you for your time and consideration.