If the null and alternative hypotheses are

Then the test is
left-tailed
two-tailed
right-tailed

To determine the type of test (left-tailed, two-tailed, or right-tailed), we need to examine the null hypothesis (denoted as \(H_0\)) and the alternative hypothesis (denoted as \(H_1\)).

- **Left-tailed test**: This occurs when the alternative hypothesis claims that a parameter is less than the null hypothesis value, i.e., \( H_1: \theta < \theta_0 \).
- **Right-tailed test**: This occurs when the alternative hypothesis claims that a parameter is greater than the null hypothesis value, i.e., \( H_1: \theta > \theta_0 \).
- **Two-tailed test**: This occurs when the alternative hypothesis claims that a parameter is not equal to the null hypothesis value, i.e., \( H_1: \theta \neq \theta_0 \).

Without seeing the explicit null and alternative hypotheses, the test type can't be identified definitively. If you provide the hypotheses, I can specify which test applies.

Would you like further clarification, or do you have the hypotheses you'd like to provide? Here are some related questions to explore:

1. What are the steps in hypothesis testing?
2. What is a p-value, and how does it relate to these tests?
3. What are Type I and Type II errors in hypothesis testing?
4. How do you interpret the results of a left-tailed test?
5. What is the difference between a z-test and a t-test?

**Tip**: Always carefully define the null and alternative hypotheses before deciding on the test type.

If the null and alternative hypotheses are
Then the test is
left-tailed
two-tailed
right-tailed

Explore the different types of hypothesis tests, including left-tailed, right-tailed, and two-tailed tests. Learn how to formulate null (H₀) and alternative (H₁) hypotheses and determine the correct test for various scenarios in statistical inference. Suitable for college-level statistics students.

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