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 45 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 = 7.60 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 n is large O the distribution of weights is normal O o is known O the distribution of weights is uniform O o is unknown (c) Interpret your results in the context of this problem. O The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99. 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 0.01. O we are 1% confident that the true average blood plasma volume in male firefighters falls within this interval.
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 45 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 = 7.60 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 n is large O the distribution of weights is normal O o is known O the distribution of weights is uniform O o is unknown (c) Interpret your results in the context of this problem. O The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99. 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 0.01. O we are 1% confident that the true average blood plasma volume in male firefighters falls within this interval.
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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Transcribed Image Text:**Total Plasma Volume Analysis for Blood Replacement Therapy**
Understanding total plasma volume is essential for determining the required plasma component in blood replacement therapy for individuals undergoing surgery. Plasma volume is influenced by overall health and physical activity.
**Sample and Assumptions:**
- A random sample of 45 male firefighters.
- Sample plasma volume mean: \( \bar{x} = 37.5 \) ml/kg.
- Standard deviation (σ) for the distribution: 7.60 ml/kg.
**Tasks:**
**(a) Calculate a 99% Confidence Interval for the Mean Plasma Volume**
1. **Lower Limit:**
2. **Upper Limit:**
3. **Margin of Error:**
Provide your answers rounded to two decimal places.
**(b) Conditions for Calculation:**
Select the necessary conditions:
- \( n \) is large
- The distribution of weights is normal
- \( \sigma \) is known
- The distribution of weights is uniform
- \( \sigma \) is unknown
**(c) Interpretation of Results:**
Select the correct interpretation:
- The probability that this interval contains the true average blood plasma volume in male firefighters is 0.99.
- 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 0.01.
- We are 1% confident that the true average blood plasma volume in male firefighters falls within this interval.
**(d) Determine Sample Size for Desired Margin of Error**
Find the sample size for a 99% confidence level with a maximal margin of error \( E = 3.00 \):
- Required sample size: (Round up to the nearest whole number)
Ensure to consider all calculations accurately for precise analysis and recommendations in a clinical setting.
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