10.2.14 An article in Quality Engineering [2012, Vol. 24(1)] described an experiment on a grinding wheel. The following are some of the grinding force data (in N) from this experiment at two different vibration levels. Low 242, 249, 235, 250, 254, 244, 258, 311, 237, 261, 314, 252 High 302, 421, 419, 399, 317, 311, 350, 363, 392, 367, 301, 302 a. Is there evidence to support the claim that the mean grind- ing force increases with the vibration level? b. Find a 95% confidence interval for the difference in the mean grinding force for the two vibration levels. c. Is the value zero contained in the 95% confidence interval? Explain the connection with the conclusion you reached in part (a). d. Do normal probability plots of grinding force indicate any violations of the assumptions for the tests and confidence interval that you performed?
10.2.14 An article in Quality Engineering [2012, Vol. 24(1)] described an experiment on a grinding wheel. The following are some of the grinding force data (in N) from this experiment at two different vibration levels. Low 242, 249, 235, 250, 254, 244, 258, 311, 237, 261, 314, 252 High 302, 421, 419, 399, 317, 311, 350, 363, 392, 367, 301, 302 a. Is there evidence to support the claim that the mean grind- ing force increases with the vibration level? b. Find a 95% confidence interval for the difference in the mean grinding force for the two vibration levels. c. Is the value zero contained in the 95% confidence interval? Explain the connection with the conclusion you reached in part (a). d. Do normal probability plots of grinding force indicate any violations of the assumptions for the tests and confidence interval that you performed?
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![**Transcription for Educational Website:**
### 10.2.14 Analysis of Grinding Force at Different Vibration Levels
An article in *Quality Engineering* [2012, Vol. 24(1)] described an experiment on a grinding wheel. Below is the grinding force data (in Newtons) from this experiment at two different vibration levels.
- **Low Vibration Level:** 242, 249, 235, 250, 254, 244, 258, 311, 237, 261, 314, 252
- **High Vibration Level:** 302, 421, 419, 399, 317, 311, 350, 363, 392, 367, 301, 302
#### Tasks
a. **Hypothesis Testing:**
- Determine whether there is evidence to support the claim that the mean grinding force increases with the vibration level.
b. **Confidence Interval Calculation:**
- Calculate a 95% confidence interval for the difference in the mean grinding force at the two vibration levels.
c. **Interpretation of Confidence Interval:**
- Check if the value zero is contained within the 95% confidence interval and explain its connection to the conclusion from part (a).
d. **Assessment of Assumptions:**
- Evaluate normal probability plots of grinding force to identify any violations of assumptions needed for the tests and confidence interval calculations.
This analysis will help in understanding how vibration levels affect grinding force and the reliability of the experimental results.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1da296ee-2468-43bb-ac80-be0eb8484519%2Fe441576b-981a-42d8-8ee6-bf5d0d761855%2Fkiagv4k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website:**
### 10.2.14 Analysis of Grinding Force at Different Vibration Levels
An article in *Quality Engineering* [2012, Vol. 24(1)] described an experiment on a grinding wheel. Below is the grinding force data (in Newtons) from this experiment at two different vibration levels.
- **Low Vibration Level:** 242, 249, 235, 250, 254, 244, 258, 311, 237, 261, 314, 252
- **High Vibration Level:** 302, 421, 419, 399, 317, 311, 350, 363, 392, 367, 301, 302
#### Tasks
a. **Hypothesis Testing:**
- Determine whether there is evidence to support the claim that the mean grinding force increases with the vibration level.
b. **Confidence Interval Calculation:**
- Calculate a 95% confidence interval for the difference in the mean grinding force at the two vibration levels.
c. **Interpretation of Confidence Interval:**
- Check if the value zero is contained within the 95% confidence interval and explain its connection to the conclusion from part (a).
d. **Assessment of Assumptions:**
- Evaluate normal probability plots of grinding force to identify any violations of assumptions needed for the tests and confidence interval calculations.
This analysis will help in understanding how vibration levels affect grinding force and the reliability of the experimental results.
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Step 1: Write the given information.
VIEWStep 2: Perform two sample variance to check whether variances for two independent samples are equal or not.
VIEWStep 3: Perform the test to claim that the mean grinding force increases with the vibration level.
VIEWStep 4: Determine the 95% confidence interval for difference in mean grinding force for two vibration level.
VIEWStep 5: Determine whether zero is contained in the 95% confidence interval.
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