When the sample standard deviation S is based on a random sample from a normal population distribution, it can be shown that E(S) = √√√2/(n − 1)Ã(n/2)σ/T((n − 1)/2) - Use this to obtain an unbiased estimator for o of the form cS. What is c when n = 18? (Round your answer to four decimal places.) X Need Help? Read It Watch It
When the sample standard deviation S is based on a random sample from a normal population distribution, it can be shown that E(S) = √√√2/(n − 1)Ã(n/2)σ/T((n − 1)/2) - Use this to obtain an unbiased estimator for o of the form cS. What is c when n = 18? (Round your answer to four decimal places.) X Need Help? Read It Watch It
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![When the sample standard deviation \( S \) is based on a random sample from a normal population distribution, it can be shown that
\[
E(S) = \sqrt{\frac{2}{(n-1)}} \frac{\Gamma(n/2)}{\Gamma((n-1)/2)} \sigma
\]
Use this to obtain an unbiased estimator for \( \sigma \) of the form \( cS \). What is \( c \) when \( n = 18 \)? (Round your answer to four decimal places.)
\[ \text{Input Box} \]
\[ \text{Incorrect answer indicator (Red X)} \]
**Need Help?**
- **Read It** (button)
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### Explanation:
This formula calculates the expected value of the sample standard deviation \( S \) for a normal population distribution. The equation uses the Gamma function \( \Gamma \) and involves the sample size \( n \).
The task is to find a constant \( c \) such that \( cS \) is an unbiased estimator for the population standard deviation \( \sigma \), specifically when \( n = 18 \). The user is prompted to input an answer, which should be rounded to four decimal places. The presence of a red "X" indicates the inputted answer is incorrect. Additionally, resources are available through "Read It" and "Watch It" buttons for further help.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4927fb7d-fe4d-496e-94ae-b9c9f1ed73cb%2F46fda046-142c-45a9-ad13-9a5b7ed8cdb4%2Fcrvq9ls_processed.png&w=3840&q=75)
Transcribed Image Text:When the sample standard deviation \( S \) is based on a random sample from a normal population distribution, it can be shown that
\[
E(S) = \sqrt{\frac{2}{(n-1)}} \frac{\Gamma(n/2)}{\Gamma((n-1)/2)} \sigma
\]
Use this to obtain an unbiased estimator for \( \sigma \) of the form \( cS \). What is \( c \) when \( n = 18 \)? (Round your answer to four decimal places.)
\[ \text{Input Box} \]
\[ \text{Incorrect answer indicator (Red X)} \]
**Need Help?**
- **Read It** (button)
- **Watch It** (button)
### Explanation:
This formula calculates the expected value of the sample standard deviation \( S \) for a normal population distribution. The equation uses the Gamma function \( \Gamma \) and involves the sample size \( n \).
The task is to find a constant \( c \) such that \( cS \) is an unbiased estimator for the population standard deviation \( \sigma \), specifically when \( n = 18 \). The user is prompted to input an answer, which should be rounded to four decimal places. The presence of a red "X" indicates the inputted answer is incorrect. Additionally, resources are available through "Read It" and "Watch It" buttons for further help.
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