Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 44 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that o = 7.40 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.) O the distribution of volumes is uniform O the distribution of volumes is normal O o is unknown On is large O o is known (c) Interpret your results in the context of this problem. O we are 99% confident that the true average blood plasma volume in male firefighters falls within this interval. O The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99. O we are 1% confident that the true average blood plasma volume in male firefighters falls within this interval. O The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01. (d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.80 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.) male firefighters
Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 44 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that o = 7.40 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.) O the distribution of volumes is uniform O the distribution of volumes is normal O o is unknown On is large O o is known (c) Interpret your results in the context of this problem. O we are 99% confident that the true average blood plasma volume in male firefighters falls within this interval. O The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99. O we are 1% confident that the true average blood plasma volume in male firefighters falls within this interval. O The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01. (d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.80 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.) male firefighters
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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![**Total Plasma Volume Analysis in Male Firefighters**
Total plasma volume is crucial in determining the necessary plasma component for blood replacement therapy in patients undergoing surgery. It is influenced by a person’s overall health and activity level. Consider a sample of 44 male firefighters, with a plasma volume sample mean of \( \bar{x} = 37.5 \) ml/kg. The standard deviation \( \sigma = 7.40 \) ml/kg for blood plasma distribution is considered.
### (a) 99% Confidence Interval Calculation
**Task:** Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. Calculate the margin of error.
- **Lower Limit:**
- **Upper Limit:**
- **Margin of Error:**
*Note: Round answers to two decimal places.*
### (b) Necessary Conditions for Calculations
Select all that apply to ensure valid statistical calculations:
- [ ] The distribution of volumes is uniform
- [ ] The distribution of volumes is normal
- [ ] \( \sigma \) is unknown
- [ ] \( n \) is large
- [ ] \( \sigma \) is known
### (c) Results Interpretation
Choose the correct interpretation:
- [ ] We are 99% confident that the true average blood plasma volume in male firefighters falls within this interval.
- [ ] The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99.
- [ ] We are 1% confident that the true average blood plasma volume in male firefighters falls within this interval.
- [ ] The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01.
### (d) Sample Size Determination
**Task:** Determine the sample size necessary for a 99% confidence level with a maximal margin of error \( E = 2.80 \) for the mean plasma volume in male firefighters.
- **Sample Size:**
*Note: Round up to the nearest whole number.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0a8d585f-99dd-4e5d-b593-c7eaddfe8ce4%2F9b39c38e-2811-40a3-9753-fc89bfe1a51e%2Fcdkn9r_processed.png&w=3840&q=75)
Transcribed Image Text:**Total Plasma Volume Analysis in Male Firefighters**
Total plasma volume is crucial in determining the necessary plasma component for blood replacement therapy in patients undergoing surgery. It is influenced by a person’s overall health and activity level. Consider a sample of 44 male firefighters, with a plasma volume sample mean of \( \bar{x} = 37.5 \) ml/kg. The standard deviation \( \sigma = 7.40 \) ml/kg for blood plasma distribution is considered.
### (a) 99% Confidence Interval Calculation
**Task:** Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. Calculate the margin of error.
- **Lower Limit:**
- **Upper Limit:**
- **Margin of Error:**
*Note: Round answers to two decimal places.*
### (b) Necessary Conditions for Calculations
Select all that apply to ensure valid statistical calculations:
- [ ] The distribution of volumes is uniform
- [ ] The distribution of volumes is normal
- [ ] \( \sigma \) is unknown
- [ ] \( n \) is large
- [ ] \( \sigma \) is known
### (c) Results Interpretation
Choose the correct interpretation:
- [ ] We are 99% confident that the true average blood plasma volume in male firefighters falls within this interval.
- [ ] The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99.
- [ ] We are 1% confident that the true average blood plasma volume in male firefighters falls within this interval.
- [ ] The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01.
### (d) Sample Size Determination
**Task:** Determine the sample size necessary for a 99% confidence level with a maximal margin of error \( E = 2.80 \) for the mean plasma volume in male firefighters.
- **Sample Size:**
*Note: Round up to the nearest whole number.*
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