Suppose that you want to compare the mean values of two independent groups (group 1 and group 2). Your hypothesis is whether the mean of group 1 is larger than the mean of group 2.

H0: μ1 < μ2, Ha: μ1 > μ2

H0: μ1 = μ2, Ha: μ1 ≠ μ2

H0: μ1 ≠ μ2, Ha: μ1 = μ2

H0: μ1 ≤ μ2, Ha: μ1 > μ2

To test whether the mean of group 1 (μ₁) is larger than the mean of group 2 (μ₂), the correct hypotheses to use would be:

- **Null Hypothesis (H₀):** μ₁ ≤ μ₂ (The mean of group 1 is less than or equal to the mean of group 2)
- **Alternative Hypothesis (Ha):** μ₁ > μ₂ (The mean of group 1 is greater than the mean of group 2)

This setup corresponds to a one-tailed test, where the goal is to determine if there is sufficient evidence to support that the mean of group 1 is greater than the mean of group 2.

**Correct Answer:**
- **H₀: μ₁ ≤ μ₂, Ha: μ₁ > μ₂**

Would you like more details or have any questions?

Here are 8 related questions to expand on this concept:

1. How do you calculate the p-value for a one-tailed hypothesis test?
2. What assumptions must be met for the t-test comparing two independent means?
3. How do you interpret the results of a hypothesis test if the p-value is very close to the significance level?
4. What is the difference between a one-tailed and a two-tailed test?
5. How do you calculate the test statistic for comparing two independent means?
6. What is the impact of sample size on the power of a hypothesis test?
7. How can you check if the variances of two groups are equal before performing a t-test?
8. What would the hypotheses look like if you were testing if the means of the two groups are different (not just greater)?

**Tip:** Always ensure the assumptions of your statistical test are met before interpreting the results, especially when dealing with hypothesis testing for comparing means.

Understand how to perform hypothesis testing to compare the means of two independent groups. Learn about setting up null and alternative hypotheses, conducting one-tailed tests, and interpreting results. Ideal for advanced undergraduate students and researchers.

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