https://file.aiquickdraw.com/mathbot/file/1736743400685ea69yzcs.jpg

To analyze the problem presented in the image, we’ll break it down step by step.

### Key Information:
1. **Claim**: The truck dealer claims that the hybrid trucks average more than 20 mpg.
2. **Null Hypothesis (H₀)**: \( \mu \leq 20 \) mpg (the average mpg is less than or equal to 20).
3. **Alternative Hypothesis (Hₐ)**: \( \mu > 20 \) mpg (the average mpg is greater than 20).
4. **Sample Statistics**:
   - Sample size (\(n\)) = 9
   - Sample mean (\(\bar{x}\)) = 22.36 mpg
   - Population standard deviation (\(\sigma\)) = 2.21 mpg
5. **Significance Level (\(\alpha\))**: 0.10 (10%).
6. **P-value**: 0.087.
   
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### Step-by-Step Analysis:

#### Step 1: Decision Rule
The significance level is 0.10. For a one-tailed test:
- If \( p\text{-value} \leq \alpha \), we reject \( H_0 \).
- If \( p\text{-value} > \alpha \), we fail to reject \( H_0 \).

#### Step 2: Compare the P-value with \(\alpha\)
Here:
- \( p\text{-value} = 0.087 \)
- \( \alpha = 0.10 \)

Since \( p\text{-value} \leq \alpha \), we **reject the null hypothesis**.

#### Step 3: Conclusion
By rejecting \( H_0 \), we have sufficient evidence to support the claim that the hybrid trucks average more than 20 mpg.

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### Best Conclusion from the Options:
The most appropriate conclusion is that the data supports the dealer’s claim that the hybrid trucks average more than 20 mpg. However, because the \( p\)-value is relatively close to the significance level, the conclusion is not extremely strong and should be considered with caution.

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Do you want further details or clarifications?  

Here are 5 related questions to expand your understanding:
1. How is the p-value calculated in hypothesis testing?
2. Why do we use a one-tailed test in this scenario instead of a two-tailed test?
3. What role does the population standard deviation play in this analysis?
4. How would the conclusion change if the significance level were reduced to 0.05?
5. How can the company improve confidence in the test results with a larger sample size?

### Tip:
Always carefully assess the p-value against the significance level and consider practical implications, especially when the p-value is close to \(\alpha\).

A company wants to verify the claim that a hybrid truck averages more than 20 mpg using sample data. Given that the sample mean is 22.36 mpg, the population standard deviation is 2.21, the p-value is 0.087, and the significance level is 10% for this one-tailed test, what is the best conclusion?

Explore how hypothesis testing is used to verify a claim about hybrid truck fuel efficiency. Given a sample mean of 22.36 mpg, a population standard deviation of 2.21 mpg, and a p-value of 0.087, we analyze the results with a significance level of 10%. This example demonstrates p-value analysis, one-tailed tests, and normal distribution properties.

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