What is the confidence interval estimate of the population mean u? ppm
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 Mercury Levels in Tuna Sushi**
**Description:**
A food safety guideline states that the mercury in fish should be below 1 part per million (ppm). Listed below are the amounts of mercury (ppm) found in tuna sushi sampled at different stores in a major city. We aim to construct a 99% confidence interval estimate of the mean amount of mercury in the population. The question we want to answer is: Does it appear that there is too much mercury in tuna sushi?
**Data:**
Mercury Levels (ppm): 0.51, 0.70, 0.10, 0.89, 1.31, 0.52, 0.96
**Question:**
What is the confidence interval estimate of the population mean \( \mu \)?
\[ \text{{ppm}} < \mu < \text{{ppm}} \]
*(Round to three decimal places as needed.)*
**Instructions:**
1. **Calculate the Mean and Standard Deviation**:
- Compute the mean of the data set.
- Calculate the standard deviation.
2. **Determine the Confidence Interval**:
- Utilize the 99% confidence level to find the critical value (z-score).
- Use the formula for the confidence interval:
\[
\bar{x} \pm (z \times \frac{s}{\sqrt{n}})
\]
Where:
- \( \bar{x} \) = sample mean
- \( z \) = z-score corresponding to 99% confidence
- \( s \) = sample standard deviation
- \( n \) = sample size
3. **Interpret the Results**:
- Analyze if the confidence interval falls entirely below 1 ppm to conclude whether the mercury level complies with safety guidelines.
4. **Tools Available**:
- Options to "Help me solve this", "View an example", and "Get more help" are available to assist in calculations or understanding the process.
Complete this task to determine whether the sampled sushi adheres to the food safety guideline for mercury levels.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff60ad45d-8a9a-4fed-88d1-40adac2a5443%2Fb1185636-83b5-4388-a122-c90b477ebae6%2Faovyeom_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Constructing a 99% Confidence Interval for Mercury Levels in Tuna Sushi**
**Description:**
A food safety guideline states that the mercury in fish should be below 1 part per million (ppm). Listed below are the amounts of mercury (ppm) found in tuna sushi sampled at different stores in a major city. We aim to construct a 99% confidence interval estimate of the mean amount of mercury in the population. The question we want to answer is: Does it appear that there is too much mercury in tuna sushi?
**Data:**
Mercury Levels (ppm): 0.51, 0.70, 0.10, 0.89, 1.31, 0.52, 0.96
**Question:**
What is the confidence interval estimate of the population mean \( \mu \)?
\[ \text{{ppm}} < \mu < \text{{ppm}} \]
*(Round to three decimal places as needed.)*
**Instructions:**
1. **Calculate the Mean and Standard Deviation**:
- Compute the mean of the data set.
- Calculate the standard deviation.
2. **Determine the Confidence Interval**:
- Utilize the 99% confidence level to find the critical value (z-score).
- Use the formula for the confidence interval:
\[
\bar{x} \pm (z \times \frac{s}{\sqrt{n}})
\]
Where:
- \( \bar{x} \) = sample mean
- \( z \) = z-score corresponding to 99% confidence
- \( s \) = sample standard deviation
- \( n \) = sample size
3. **Interpret the Results**:
- Analyze if the confidence interval falls entirely below 1 ppm to conclude whether the mercury level complies with safety guidelines.
4. **Tools Available**:
- Options to "Help me solve this", "View an example", and "Get more help" are available to assist in calculations or understanding the process.
Complete this task to determine whether the sampled sushi adheres to the food safety guideline for mercury levels.
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