Two fuel additives are tested to determine their effect on miles per gallon for passenger cars. Test results for 12 cars follow; each car was tested with both fuel additives. Additive

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## Investigation of Fuel Additives on Vehicle Efficiency

Two fuel additives are assessed to determine their effects on miles per gallon (mpg) for passenger cars. Results for 12 cars are provided, each tested with both additives.

| Car | Additive 1 | Additive 2 |
|-----|------------|------------|
| 1   | 20.12      | 18.05      |
| 2   | 23.56      | 20.77      |
| 3   | 21.03      | 21.57      |
| 4   | 19.15      | 16.06      |
| 5   | 21.23      | 20.22      |
| 6   | 24.77      | 23.8       |
| 7   | 16.16      | 16.16      |
| 8   | 18.55      | 13.98      |
| 9   | 20.87      | 20.03      |
| 10  | 23.23      | 21.15      |
| 11  | 23.21      | 21.78      |
| 12  | 24.02      | 22.7       |

### Statistical Testing

Utilizing a significance level of α = 0.05, the Wilcoxon signed-rank test is employed to evaluate whether there is a significant difference between the median mpg for the additives.

#### a. Hypotheses

- **Null Hypothesis (H₀):** Median for Additive 1 minus Median for Additive 2 equals 0
- **Alternative Hypothesis (H₁):** Median for Additive 1 minus Median for Additive 2 does not equal 0

Both hypotheses are correctly stated with checkmarks next to them.

#### b. Mean and Standard Deviation

- **Mean:** 39 ✓
- **Standard Deviation:** 25.4951 ✗ (incorrect)

These values pertain to the distribution used in the statistical analysis.
Transcribed Image Text:## Investigation of Fuel Additives on Vehicle Efficiency Two fuel additives are assessed to determine their effects on miles per gallon (mpg) for passenger cars. Results for 12 cars are provided, each tested with both additives. | Car | Additive 1 | Additive 2 | |-----|------------|------------| | 1 | 20.12 | 18.05 | | 2 | 23.56 | 20.77 | | 3 | 21.03 | 21.57 | | 4 | 19.15 | 16.06 | | 5 | 21.23 | 20.22 | | 6 | 24.77 | 23.8 | | 7 | 16.16 | 16.16 | | 8 | 18.55 | 13.98 | | 9 | 20.87 | 20.03 | | 10 | 23.23 | 21.15 | | 11 | 23.21 | 21.78 | | 12 | 24.02 | 22.7 | ### Statistical Testing Utilizing a significance level of α = 0.05, the Wilcoxon signed-rank test is employed to evaluate whether there is a significant difference between the median mpg for the additives. #### a. Hypotheses - **Null Hypothesis (H₀):** Median for Additive 1 minus Median for Additive 2 equals 0 - **Alternative Hypothesis (H₁):** Median for Additive 1 minus Median for Additive 2 does not equal 0 Both hypotheses are correctly stated with checkmarks next to them. #### b. Mean and Standard Deviation - **Mean:** 39 ✓ - **Standard Deviation:** 25.4951 ✗ (incorrect) These values pertain to the distribution used in the statistical analysis.
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