Need help with this and thak you in advance!Here's the Data:Rod Length25.4225.8925.2124.3224.7024.1524.4923.2924.1325.7124.6523.2024.8025.9523.4725.8024.2425.2325.1625.2224.5924.5324.7024.8124.4023.4525.2824.0324.3425.1326.0825.7423.7124.1825.1126.2925.6125.4724.3624.5924.2424.9425.9424.1326.1225.1624.8323.4724.9625.3426.0025.1925.6124.6624.4824.6425.9724.4024.5524.1324.8325.6024.6326.0023.5624.5624.3825.1224.9025.8325.4424.9824.8125.0924.2524.0025.9025.4624.3025.2223.3224.5825.6024.7125.8523.2225.8224.9824.9524.2324.6924.4424.0525.1225.2124.9824.2125.8925.2324.8924.9125.7625.6124.8424.8324.1625.7024.5624.8424.2525.4524.1525.0025.2326.0025.2224.0624.9424.7925.0425.7424.9125.6624.5726.7323.2225.8524.2924.6825.2925.7124.6324.4325.9625.5224.7124.3625.1124.4525.8724.7224.2324.7425.5925.4524.3925.4624.0725.3925.50 ## Statistical Analysis of Manufacturing Data### ObjectiveA factory manufactures steel rods, which are supposed to have a mean length of 25 cm. If evidence at $\alpha = 0.05$ shows the mean length is different from 25 cm, the factory will shut down due to potential customer dissatisfaction and maintenance issues. A random sample of 150 rods is taken, with lengths provided in the file **rods20.xls**.### Tasks1. **Make a Frequency Table and Histogram** - Organize the data with the first class of lengths (20, 23.5). 2. **Conduct a Hypothesis Test** - Test if the mean length of the rods is different from 25 cm.3. **Conclusions and Recommendations** - Based on the test results, decide if shutting down the factory is necessary. 4. **Understanding Errors** - Define: - **Type I Error**: Rejecting a true null hypothesis (false positive). - **Type II Error**: Failing to reject a false null hypothesis (false negative). 5. **Error Consequences** - Discuss potential outcomes of making Type I and Type II errors in this context. 6. **Confidence Interval** - Find and interpret a 95% confidence interval for the rod lengths.7. **Final Recommendations** - Decide on shutting down the factory based on the confidence interval. Justify your decision. 8. **Comparative Analysis** - Compare and contrast conclusions from hypothesis testing and confidence intervals.### Notes- **Goal**: Use the data for practical learning.- **Data Management**: Save all files and data diligently.### Lab Report Requirements- Include frequency table, histogram, and hypothesis tests in your report.- Report both the test statistic and p-value, decide on $H_0$, and summarize your findings.- Use accurate and concise data representation—include tables and graphs for clarity.- Precision: Use thousandths where applicable. Remember, thorough preparation and analysis in this project are critical for practical learning and decision-making in a manufacturing context.

Name: Need help with this and thak you in advance!Here's the Data:Rod Length
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Description: Need help with this and thak you in advance!Here's the Data:Rod Length25.4225.8925.2124.3224.7024.1524.4923.2924.1325.7124.6523.2024.8025.9523.4725.8024.2425.2325.1625.2224.5924.5324.7024.8124.4023.4525.2824.0324.3425.1326.0825.7423.7124.1825.1126.29

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Answered: Need help with this and thak you in…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 2AGP

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Need help with this and thak you in advance!

Here's the Data:

Rod Length
25.42
25.89
25.21
24.32
24.70
24.15
24.49
23.29
24.13
25.71
24.65
23.20
24.80
25.95
23.47
25.80
24.24
25.23
25.16
25.22
24.59
24.53
24.70
24.81
24.40
23.45
25.28
24.03
24.34
25.13
26.08
25.74
23.71
24.18
25.11
26.29
25.61
25.47
24.36
24.59
24.24
24.94
25.94
24.13
26.12
25.16
24.83
23.47
24.96
25.34
26.00
25.19
25.61
24.66
24.48
24.64
25.97
24.40
24.55
24.13
24.83
25.60
24.63
26.00
23.56
24.56
24.38
25.12
24.90
25.83
25.44
24.98
24.81
25.09
24.25
24.00
25.90
25.46
24.30
25.22
23.32
24.58
25.60
24.71
25.85
23.22
25.82
24.98
24.95
24.23
24.69
24.44
24.05
25.12
25.21
24.98
24.21
25.89
25.23
24.89
24.91
25.76
25.61
24.84
24.83
24.16
25.70
24.56
24.84
24.25
25.45
24.15
25.00
25.23
26.00
25.22
24.06
24.94
24.79
25.04
25.74
24.91
25.66
24.57
26.73
23.22
25.85
24.29
24.68
25.29
25.71
24.63
24.43
25.96
25.52
24.71
24.36
25.11
24.45
25.87
24.72
24.23
24.74
25.59
25.45
24.39
25.46
24.07
25.39
25.50

## Statistical Analysis of Manufacturing Data

### Objective

A factory manufactures steel rods, which are supposed to have a mean length of 25 cm. If evidence at $\alpha = 0.05$ shows the mean length is different from 25 cm, the factory will shut down due to potential customer dissatisfaction and maintenance issues. A random sample of 150 rods is taken, with lengths provided in the file **rods20.xls**.

### Tasks

1. **Make a Frequency Table and Histogram**
- Organize the data with the first class of lengths (20, 23.5).

2. **Conduct a Hypothesis Test**
- Test if the mean length of the rods is different from 25 cm.

3. **Conclusions and Recommendations**
- Based on the test results, decide if shutting down the factory is necessary.

4. **Understanding Errors**
- Define:
- **Type I Error**: Rejecting a true null hypothesis (false positive).
- **Type II Error**: Failing to reject a false null hypothesis (false negative).

5. **Error Consequences**
- Discuss potential outcomes of making Type I and Type II errors in this context.

6. **Confidence Interval**
- Find and interpret a 95% confidence interval for the rod lengths.

7. **Final Recommendations**
- Decide on shutting down the factory based on the confidence interval. Justify your decision.

8. **Comparative Analysis**
- Compare and contrast conclusions from hypothesis testing and confidence intervals.

### Notes

- **Goal**: Use the data for practical learning.
- **Data Management**: Save all files and data diligently.

### Lab Report Requirements

- Include frequency table, histogram, and hypothesis tests in your report.
- Report both the test statistic and p-value, decide on $H_0$, and summarize your findings.
- Use accurate and concise data representation—include tables and graphs for clarity.
- Precision: Use thousandths where applicable.

Remember, thorough preparation and analysis in this project are critical for practical learning and decision-making in a manufacturing context.

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