MATLAB: An Introduction with Applications
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Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Transcribed Image Text:The image shows a text problem focused on statistical analysis, specifically about finding a confidence interval for a population mean. Here's a transcription suitable for an educational website:
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**Plasma Volume Analysis**
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 40 male firefighters is tested and that they have a plasma volume sample mean of \( x = 37.5 \, \text{ml/kg} \) (milliliters plasma per kilogram body weight). Assume that \( \sigma = 7.10 \, \text{ml/kg} \) for the distribution of blood plasma.
*When finding a 99% confidence interval, what is the critical value for the confidence level? (Give your answer to two decimal places.)*
\( Z_c = \)
**(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.)
- \( n \) is large
- The distribution of volumes is normal
- \( \sigma \) is unknown
- The distribution of volumes is uniform
- \( \sigma \) is known
**(c)** Interpret your results in the context of this problem.
- We are 99% confident that the true average blood plasma volume in male firefighters falls within this interval.
- 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 0.99.
- The probability that this interval contains the true average blood plasma volume in male firefighters is 0.01.
**(d)** Which equation is used to find the sample size \( n \) for estimating \( \mu \) when \( \sigma \) is known?
- \( n = \left( \frac{Z_c E}{\sigma} \right)^2 \)
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This content would help students understand the statistical methods involved in analyzing blood plasma volumes using a confidence interval approach.
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