The given problem involves hypothesis testing, specifically a two-tailed t-test.

Problem Analysis:

1. Null Hypothesis (H₀): μ₁ - μ₂ = 0
2. Alternative Hypothesis (H₁): μ₁ - μ₂ ≠ 0
3. The test statistic value, t = 2.34, is given.
4. The decision depends on comparing the test statistic with the critical t-value at the given significance level (α).

Given Answers:

1. Critical t-values are provided for different α levels: 0.05, 0.02, and 0.01.
2. Compare $|t| = 2.34$ with these critical values.

Solution:

• At α = 0.05, the critical value is 2.086. Since $2.34 > 2.086$, reject H₀.
• At α = 0.02, the critical value is 2.528. Since $2.34 < 2.528$, fail to reject H₀.
• At α = 0.01, the critical value is 2.552. Since $2.34 < 2.552$, fail to reject H₀.

Thus, the correct decision is:

• Reject the null hypothesis at α = 0.05 because 2.34 > 2.086.

Correct Answer:

Option 1: "Reject the null hypothesis at α = 0.05 because 2.34 > 2.086."

Let me know if you have any questions or would like further clarification!

Related Questions:

1. What are the steps to conduct a two-tailed t-test?
2. How do you determine the degrees of freedom in a t-test?
3. Why is the null hypothesis rejected when the test statistic exceeds the critical value?
4. How does the significance level affect hypothesis test results?
5. What is the difference between a one-tailed and a two-tailed t-test?

Tip: Always verify the critical t-value using degrees of freedom and the chosen α-level.