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.

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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.