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%
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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fccb668bc-10a4-4aaf-a388-7b2b8ddb3a25%2F78cff506-79e9-4084-88ea-6978a2390901%2Fpzaerpr_processed.png&w=3840&q=75)
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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