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.