MATLAB: An Introduction with Applications
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Author: Amos Gilat
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Transcribed Image Text:**Topic: Statistical Analysis of Uric Acid Levels**
Overproduction of uric acid in the body can be an indication of cell breakdown. This may indicate illnesses such as gout, leukemia, or lymphoma. Over a period of months, an adult male patient has taken eleven blood tests for uric acid. The mean concentration was \(\bar{x} = 5.31 \, \text{mg/dl}\). The distribution of uric acid in healthy adult males can be assumed to be normal, with \(\sigma = 1.79 \, \text{mg/dl}\).
**(a) Confidence Interval Calculation**
- Calculate the 95% confidence interval for the population mean concentration of uric acid in this patient’s blood.
- Determine the margin of error. (Round answers to two decimal places.)
| Lower Limit | Upper Limit | Margin of Error |
|-------------|-------------|-----------------|
| | | |
**(b) Necessary Conditions for Calculation**
- Select all applicable conditions:
- \(\sigma\) is known
- \(\sigma\) is unknown
- Uniform distribution of uric acid
- \(n\) is large
- Normal distribution of uric acid
**(c) Interpretation of Results**
- Choose the correct interpretation:
- The probability that this interval contains the true average uric acid level for this patient is 0.95.
- The probability that this interval contains the true average uric acid level for this patient is 0.05.
- We are 95% confident that the true uric acid level for this patient falls within this interval.
- We are 5% confident that the true uric acid level for this patient falls within this interval.
**(d) Sample Size Calculation**
- Find the sample size necessary for a 95% confidence level with a maximal margin of error \(E = 1.10\) for the mean concentration of uric acid in this patient's blood. (Round your answer up to the nearest whole number.)
| Number of blood tests |
|-----------------------|
This exercise helps in understanding how to calculate and interpret confidence intervals in the context of medical testing and diagnosis.
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