Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
Sure, let's analyze the given data and calculate the Spearman's Rank correlation coefficient for each combination of the production techniques. The Spearman's Rank correlation coefficient is a measure of the strength and direction of association between two ranked variables.
### Data Set:
We have the following data:
| Worker | Technique 1 | Technique 2 | Technique 3 |
|--------|-------------|-------------|-------------|
| A | 40 | 60 | 55 |
| B | 50 | 86 | 65 |
| C | 55 | 40 | 40 |
| D | 60 | 59 | 42 |
| E | 63 | 62 | 85 |
| F | 57 | 85 | 70 |
| G | 42 | 90 | 73 |
| H | 69 | 42 | 47 |
| I | 80 | 40 | 90 |
| S | 44 | | 64 |
(Note: Worker S does not have data for Technique 2, hence calculations with this entry will exclude this specific technique.)
To find the Spearman's Rank correlation coefficient, we follow these steps for each pair of techniques:
1. Rank the data for each technique.
2. Compute the difference in ranks for each pair of techniques.
3. Calculate the square of the differences.
4. Use the formula for Spearman's Rank correlation coefficient:
[tex]\[ \rho = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)} \][/tex]
where [tex]\( d_i \)[/tex] is the difference between ranks for each pair of observations and [tex]\( n \)[/tex] is the number of observations.
Given the calculations:
### Technique 1 and Technique 2:
- Spearman's Rank correlation coefficient: -0.5607 (approx.)
### Technique 1 and Technique 3:
- Spearman's Rank correlation coefficient: 0.2000 (approx.)
### Technique 2 and Technique 3:
- Spearman's Rank correlation coefficient: 0.3347 (approx.)
### Conclusion:
The Spearman's Rank correlation coefficient is highest between Technique 2 and Technique 3 with a value of 0.3347. Thus, the firm should consider this pair of production techniques as the most efficient based on their higher correlation.
In summary:
- Correlation coefficient for Technique 1 and Technique 2 is approximately -0.5607.
- Correlation coefficient for Technique 1 and Technique 3 is approximately 0.2000.
- Correlation coefficient for Technique 2 and Technique 3 is approximately 0.3347.
- Best combination of techniques with the highest Spearman's Rank correlation coefficient is Technique 2 and Technique 3.
### Data Set:
We have the following data:
| Worker | Technique 1 | Technique 2 | Technique 3 |
|--------|-------------|-------------|-------------|
| A | 40 | 60 | 55 |
| B | 50 | 86 | 65 |
| C | 55 | 40 | 40 |
| D | 60 | 59 | 42 |
| E | 63 | 62 | 85 |
| F | 57 | 85 | 70 |
| G | 42 | 90 | 73 |
| H | 69 | 42 | 47 |
| I | 80 | 40 | 90 |
| S | 44 | | 64 |
(Note: Worker S does not have data for Technique 2, hence calculations with this entry will exclude this specific technique.)
To find the Spearman's Rank correlation coefficient, we follow these steps for each pair of techniques:
1. Rank the data for each technique.
2. Compute the difference in ranks for each pair of techniques.
3. Calculate the square of the differences.
4. Use the formula for Spearman's Rank correlation coefficient:
[tex]\[ \rho = 1 - \frac{6 \sum d_i^2}{n(n^2 - 1)} \][/tex]
where [tex]\( d_i \)[/tex] is the difference between ranks for each pair of observations and [tex]\( n \)[/tex] is the number of observations.
Given the calculations:
### Technique 1 and Technique 2:
- Spearman's Rank correlation coefficient: -0.5607 (approx.)
### Technique 1 and Technique 3:
- Spearman's Rank correlation coefficient: 0.2000 (approx.)
### Technique 2 and Technique 3:
- Spearman's Rank correlation coefficient: 0.3347 (approx.)
### Conclusion:
The Spearman's Rank correlation coefficient is highest between Technique 2 and Technique 3 with a value of 0.3347. Thus, the firm should consider this pair of production techniques as the most efficient based on their higher correlation.
In summary:
- Correlation coefficient for Technique 1 and Technique 2 is approximately -0.5607.
- Correlation coefficient for Technique 1 and Technique 3 is approximately 0.2000.
- Correlation coefficient for Technique 2 and Technique 3 is approximately 0.3347.
- Best combination of techniques with the highest Spearman's Rank correlation coefficient is Technique 2 and Technique 3.
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.
