Please use the accompanying Excel data set or accompanying Text file data set when completing the following exercise. An article in the Journal of Aircraft (1986, Vol.23, pp. 859-864) described a new equivalent plate analysis method formulation that is capable of modeling aircraft structures such as cranked wing boxes and that produces results similar to the more computationally intensive finite element analysis method, Natural vibration frequencies for the cranked wing box structure are calculated using both methods, and results for the first seven natural frequencies follow: Frequency Finite Element, Cycles Equivalent Plate, Cycles 1 14.58 2 3 4 5 6 7 48.52 97.21 113.99 174,73 212.72 277.38 14.76 49.10 99.99 Yes, the equivalent plate method is better since all of the values in the intervalore negative No, there is no significant difference between the two methods 117.53 181.22 220.14 294.80 Use only Table V of Appendix A. (a) De the data suggest that the two methods provide the same mean value for natural vibration frequency? Find interval for P-value:

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### Transcription for Educational Website

**Title: Comparative Analysis of Natural Vibration Frequencies in Aviation Structures**

**Introduction:**
An article in the *Journal of Aircraft* (1986, Vol. 23, pp. 859-864) introduced a new equivalent plate analysis method for modeling aircraft structures, specifically cranked wing boxes. This method provides results similar to the computationally intensive finite element analysis method. Below is a table displaying the natural vibration frequencies for the cranked wing box structure calculated using both methods for the first seven natural frequencies.

**Table: Vibration Frequency Analysis**

| Frequency | Finite Element, Cycles/s | Equivalent Plate, Cycles/s |
|-----------|--------------------------|----------------------------|
| 1         | 14.58                    | 14.76                      |
| 2         | 48.52                    | 49.10                      |
| 3         | 97.21                    | 99.99                      |
| 4         | 113.99                   | 117.53                     |
| 5         | 174.73                   | 181.22                     |
| 6         | 212.72                   | 220.14                     |
| 7         | 277.38                   | 294.80                     |

**Analysis Exercise:**

**(a) Hypothesis Testing:**
- **Question:** Do the data suggest that the two methods provide the same mean value for natural vibration frequency?
- **Action:** Find the interval for P-value:
  - <select P-value> <  [options with intervals]
- **Conclusion:** For a significance level of α = 0.05:
  - [Select conclusion option with drop-down]
  - Determine if there's sufficient evidence to conclude that the two methods provide different mean values for natural vibration frequency.

**(b) Confidence Interval:**
- **Task:** Find a 95% confidence interval on the mean difference between the two methods and use it to answer the question in part (a).
- Round your answer to 3 decimal places.

**Conclusion:**
- **Question:** Does the confidence interval indicate that the two methods provide different mean values for natural vibration frequency?
  - [Conclusion options with drop-down]
  - Explanation based on confidence interval analysis.

**Note:**
- Use only Table V of Appendix A.
- Options provided for conclusions are based on statistical outcomes derived from the analysis.

**Resource:**
-
Transcribed Image Text:### Transcription for Educational Website **Title: Comparative Analysis of Natural Vibration Frequencies in Aviation Structures** **Introduction:** An article in the *Journal of Aircraft* (1986, Vol. 23, pp. 859-864) introduced a new equivalent plate analysis method for modeling aircraft structures, specifically cranked wing boxes. This method provides results similar to the computationally intensive finite element analysis method. Below is a table displaying the natural vibration frequencies for the cranked wing box structure calculated using both methods for the first seven natural frequencies. **Table: Vibration Frequency Analysis** | Frequency | Finite Element, Cycles/s | Equivalent Plate, Cycles/s | |-----------|--------------------------|----------------------------| | 1 | 14.58 | 14.76 | | 2 | 48.52 | 49.10 | | 3 | 97.21 | 99.99 | | 4 | 113.99 | 117.53 | | 5 | 174.73 | 181.22 | | 6 | 212.72 | 220.14 | | 7 | 277.38 | 294.80 | **Analysis Exercise:** **(a) Hypothesis Testing:** - **Question:** Do the data suggest that the two methods provide the same mean value for natural vibration frequency? - **Action:** Find the interval for P-value: - <select P-value> < [options with intervals] - **Conclusion:** For a significance level of α = 0.05: - [Select conclusion option with drop-down] - Determine if there's sufficient evidence to conclude that the two methods provide different mean values for natural vibration frequency. **(b) Confidence Interval:** - **Task:** Find a 95% confidence interval on the mean difference between the two methods and use it to answer the question in part (a). - Round your answer to 3 decimal places. **Conclusion:** - **Question:** Does the confidence interval indicate that the two methods provide different mean values for natural vibration frequency? - [Conclusion options with drop-down] - Explanation based on confidence interval analysis. **Note:** - Use only Table V of Appendix A. - Options provided for conclusions are based on statistical outcomes derived from the analysis. **Resource:** -
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