An automobile manufacturer has given its van a 33.3
 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van performs under the manufacturer's MPG rating. After testing 210
 vans, they found a mean MPG of 33.1
. Assume the population standard deviation is known to be 1.9
. Is there sufficient evidence at the 0.05
 level to support the testing firm's claim?

Step 3 of 6 :  Specify if the test is one-tailed or two-tailed.

This test is a **one-tailed test**.

### Explanation:
The claim is that the van performs **under** the manufacturer's MPG rating of 33.3. A one-tailed test is used when the hypothesis specifically checks for a decrease (or increase) in the parameter.

- **Null Hypothesis (\(H_0\))**: The van's MPG is at least 33.3 (\(\mu \geq 33.3\)).
- **Alternative Hypothesis (\(H_a\))**: The van's MPG is less than 33.3 (\(\mu < 33.3\)).

Since the alternative hypothesis (\(H_a\)) is directional (\(\mu < 33.3\)), this makes it a **one-tailed test**. 

Let me know if you'd like further clarification or assistance with the next steps! 

### Questions:
1. What is the critical z-value for a one-tailed test at the 0.05 significance level?
2. How do we calculate the z-test statistic in this scenario?
3. What would the p-value represent in this context, and how is it interpreted?
4. What are the consequences of incorrectly choosing a two-tailed test here?
5. Why is the standard deviation considered known in this problem?

### Tip:
In hypothesis testing, clearly identifying the direction of the claim ensures that the appropriate test type (one-tailed or two-tailed) is selected. Misidentifying this can lead to incorrect conclusions.

An automobile manufacturer has given its van a 33.3 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van performs under the manufacturer's MPG rating. After testing 210 vans, they found a mean MPG of 33.1. Assume the population standard deviation is known to be 1.9. Is there sufficient evidence at the 0.05 level to support the testing firm's claim? Step 3 of 6: Specify if the test is one-tailed or two-tailed.

Explore how to determine if a one-tailed test is appropriate in hypothesis testing for an automobile's MPG rating. Learn the key steps, including hypothesis formulation, the use of z-test formulas, and interpretation of significance levels. This problem involves testing whether the MPG is less than the manufacturer's claim of 33.3 MPG, based on data from 210 vans.

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