3. Which of the following sets of hypotheses is associated with a two-tailed test? Но: и < 12 На: ш< 12 Но: и< 12 На: и> 12 Но: и 3 12 На: д # 12 all of the above are correct

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**Question 3: Which of the following sets of hypotheses is associated with a two-tailed test?**

- \( H_0: \mu < 12 \quad H_a: \mu \leq 12 \)

- \( H_0: \mu \leq 12 \quad H_a: \mu > 12 \)

- \( H_0: \mu = 12 \quad H_a: \mu \neq 12 \)

- all of the above are correct

**Explanation:**

For a two-tailed test, the null hypothesis (\( H_0 \)) is typically that the parameter is equal to a certain value, while the alternative hypothesis (\( H_a \)) states that the parameter is not equal to that value. This is represented by option 3: 

- \( H_0: \mu = 12 \)
- \( H_a: \mu \neq 12 \)

This option checks for deviations in both directions from the hypothesized value (both less than and greater than). Therefore, option 3 is the correct set associated with a two-tailed test.
Transcribed Image Text:**Question 3: Which of the following sets of hypotheses is associated with a two-tailed test?** - \( H_0: \mu < 12 \quad H_a: \mu \leq 12 \) - \( H_0: \mu \leq 12 \quad H_a: \mu > 12 \) - \( H_0: \mu = 12 \quad H_a: \mu \neq 12 \) - all of the above are correct **Explanation:** For a two-tailed test, the null hypothesis (\( H_0 \)) is typically that the parameter is equal to a certain value, while the alternative hypothesis (\( H_a \)) states that the parameter is not equal to that value. This is represented by option 3: - \( H_0: \mu = 12 \) - \( H_a: \mu \neq 12 \) This option checks for deviations in both directions from the hypothesized value (both less than and greater than). Therefore, option 3 is the correct set associated with a two-tailed test.
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