14. Your investment executive claims that the average yearly rate of return on the stocks she recommends is at least 10.0%. You plan on taking a sample to test her claim. The correct set of hypotheses is Ho: u > 10.0% Ha: µ s 10.0% Ho: u z 10.0% Ha: u < 10.0% Но: и < 10.0% На: и 2 10.0% H0: u s 10.0% Ha: µ > 10.0%

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**Transcription for Educational Website:**

Title: Hypothesis Testing for Investment Returns

---

**Question 14:**

Your investment executive claims that the average yearly rate of return on the stocks she recommends is at least 10.0%. You plan on taking a sample to test her claim. The correct set of hypotheses is _____.

**Options:**

- ○ \(H_0: \mu > 10.0\% \quad H_a: \mu \leq 10.0\%\)

- ○ \(H_0: \mu \geq 10.0\% \quad H_a: \mu < 10.0\%\)

- ○ \(H_0: \mu < 10.0\% \quad H_a: \mu \geq 10.0\%\)

- ● \(H_0: \mu \leq 10.0\% \quad H_a: \mu > 10.0\%\) (Correct Option Highlighted)

**Explanation:**

To test the claim that the average yearly rate of return is at least 10.0%, we set up the null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_a\)) as follows:

- **Null Hypothesis (\(H_0\))**: The average rate of return is less than or equal to 10.0% (\(\mu \leq 10.0\%\)).
  
- **Alternative Hypothesis (\(H_a\))**: The average rate of return is greater than 10.0% (\(\mu > 10.0\%\)).

This setup tests whether the returns are significantly greater than 10.0%, which aligns with the executive's claim. 

(Note: Even though one option closely aligns with the executive's claim of “at least 10.0%," the hypothesis must test for the possibility that it is greater than 10.0% to be valid against the null of it being no greater.)
Transcribed Image Text:**Transcription for Educational Website:** Title: Hypothesis Testing for Investment Returns --- **Question 14:** Your investment executive claims that the average yearly rate of return on the stocks she recommends is at least 10.0%. You plan on taking a sample to test her claim. The correct set of hypotheses is _____. **Options:** - ○ \(H_0: \mu > 10.0\% \quad H_a: \mu \leq 10.0\%\) - ○ \(H_0: \mu \geq 10.0\% \quad H_a: \mu < 10.0\%\) - ○ \(H_0: \mu < 10.0\% \quad H_a: \mu \geq 10.0\%\) - ● \(H_0: \mu \leq 10.0\% \quad H_a: \mu > 10.0\%\) (Correct Option Highlighted) **Explanation:** To test the claim that the average yearly rate of return is at least 10.0%, we set up the null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_a\)) as follows: - **Null Hypothesis (\(H_0\))**: The average rate of return is less than or equal to 10.0% (\(\mu \leq 10.0\%\)). - **Alternative Hypothesis (\(H_a\))**: The average rate of return is greater than 10.0% (\(\mu > 10.0\%\)). This setup tests whether the returns are significantly greater than 10.0%, which aligns with the executive's claim. (Note: Even though one option closely aligns with the executive's claim of “at least 10.0%," the hypothesis must test for the possibility that it is greater than 10.0% to be valid against the null of it being no greater.)
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