Samples of DNA are collected, and the four DNA bases of A, G, C, and T are coded as 1, 2, 3, and 4, respectively. The results are listed below. Construct a 99% confidence interval estimate of the mean. What is the practical use of the confidence interval? 1, 1, 2, 4, 3, 3, 3, 4, 4, 2 D What is the confidence interval for the population mean u?
Samples of DNA are collected, and the four DNA bases of A, G, C, and T are coded as 1, 2, 3, and 4, respectively. The results are listed below. Construct a 99% confidence interval estimate of the mean. What is the practical use of the confidence interval? 1, 1, 2, 4, 3, 3, 3, 4, 4, 2 D What is the confidence interval for the population mean u?
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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![**Title: Constructing a 99% Confidence Interval for DNA Base Coding**
**Description:**
In this exercise, we explore the process of constructing a 99% confidence interval for the mean of coded DNA bases. Samples of DNA are collected, and the four DNA bases, adenine (A), guanine (G), cytosine (C), and thymine (T), are numerically coded as 1, 2, 3, and 4, respectively.
**Dataset:**
The results are as follows: 1, 1, 2, 4, 3, 3, 3, 4, 4, 2
**Objective:**
The task is to construct a 99% confidence interval estimate of the mean. Additionally, discuss the practical use of the confidence interval.
**Instructions:**
1. Calculate the sample mean (\( \overline{x} \)).
2. Determine the standard deviation of the sample.
3. Use the appropriate z-score for a 99% confidence interval.
4. Construct the confidence interval using the formula:
\[
\text{Confidence Interval} = \overline{x} \pm z \times \left(\frac{\sigma}{\sqrt{n}}\right)
\]
where \( n \) is the sample size.
5. Interpret the confidence interval: What does this interval tell us about the population mean \( \mu \)?
**Input:**
The user is prompted to input the computed confidence interval:
\[
\_\_\_ < \mu < \_\_\_ \quad (\text{Round to one decimal place as needed.})
\]
**Interactive Elements:**
- "Help me solve this" offers guidance on the steps to calculate the confidence interval.
- "View an example" provides a similar example with detailed solution steps.
- "Get more help" links to additional resources on confidence intervals and statistical analysis.
**Practical Use:**
Understanding the confidence interval provides insight into the reliability of the estimated mean for the coded DNA bases. This can be particularly useful in genetic studies and research involving DNA sequence analysis.
**Toolbar Options:**
- **Clear all**: Resets the input fields.
- **Check answer**: Verifies the user's calculated confidence interval.
**Note:**
It is important to round the confidence interval to one decimal place as indicated for precision in reporting.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff60ad45d-8a9a-4fed-88d1-40adac2a5443%2Fada62b8f-b901-4af0-92e6-30e5ca0fa108%2Fqucuhau_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Constructing a 99% Confidence Interval for DNA Base Coding**
**Description:**
In this exercise, we explore the process of constructing a 99% confidence interval for the mean of coded DNA bases. Samples of DNA are collected, and the four DNA bases, adenine (A), guanine (G), cytosine (C), and thymine (T), are numerically coded as 1, 2, 3, and 4, respectively.
**Dataset:**
The results are as follows: 1, 1, 2, 4, 3, 3, 3, 4, 4, 2
**Objective:**
The task is to construct a 99% confidence interval estimate of the mean. Additionally, discuss the practical use of the confidence interval.
**Instructions:**
1. Calculate the sample mean (\( \overline{x} \)).
2. Determine the standard deviation of the sample.
3. Use the appropriate z-score for a 99% confidence interval.
4. Construct the confidence interval using the formula:
\[
\text{Confidence Interval} = \overline{x} \pm z \times \left(\frac{\sigma}{\sqrt{n}}\right)
\]
where \( n \) is the sample size.
5. Interpret the confidence interval: What does this interval tell us about the population mean \( \mu \)?
**Input:**
The user is prompted to input the computed confidence interval:
\[
\_\_\_ < \mu < \_\_\_ \quad (\text{Round to one decimal place as needed.})
\]
**Interactive Elements:**
- "Help me solve this" offers guidance on the steps to calculate the confidence interval.
- "View an example" provides a similar example with detailed solution steps.
- "Get more help" links to additional resources on confidence intervals and statistical analysis.
**Practical Use:**
Understanding the confidence interval provides insight into the reliability of the estimated mean for the coded DNA bases. This can be particularly useful in genetic studies and research involving DNA sequence analysis.
**Toolbar Options:**
- **Clear all**: Resets the input fields.
- **Check answer**: Verifies the user's calculated confidence interval.
**Note:**
It is important to round the confidence interval to one decimal place as indicated for precision in reporting.
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