Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma.† Over a period of months, an adult male patient has taken seven blood tests for uric acid. The mean concentration was x = 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal, with σ = 1.77 mg/dl.
(a) Find a 95% confidence interval for the population mean concentration of uric acid in this patient's blood. 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.)
uniform distribution of uric acidnormal distribution of uric acidn is largeσ is knownσ is unknown
(c) Interpret your results in the context of this problem.
The probability that this interval contains the true average uric acid level for this patient is 0.05.The probability that this interval contains the true average uric acid level for this patient is 0.95. 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) Find the sample size necessary for a 95% confidence level with
maximal margin of error E = 1.20 for the mean
concentration of uric acid in this patient's blood. (Round your
answer up to the nearest whole number.)
blood tests
using excel>Addin>phstat>confidence interval
we have
Confidence Interval Estimate for the Mean | |
Data | |
Population Standard Deviation | 1.77 |
Sample Mean | 5.35 |
Sample Size | 7 |
Confidence Level | 95% |
Intermediate Calculations | |
Standard Error of the Mean | 0.6690 |
Z Value | -1.9600 |
Interval Half Width | 1.3112 |
Confidence Interval | |
Interval Lower Limit | 4.04 |
Interval Upper Limit | 6.66 |
lower limit | 1.31 |
upper limit | 4.04 |
margin of error | 6.66 |
(b) conditions are necessary for your calculations
normal distribution of uric acid σ is known
(c) Interpret your results in the context of this problem.
We are 95% confident that the true uric acid level for this patient falls within this interval
(d) using excel>addin>phstat>sample size determination
we have
Sample Size Determination | |
Data | |
Population Standard Deviation | 1.77 |
Sampling Error | 1.2 |
Confidence Level | 95% |
Intemediate Calculations | |
Z Value | -1.9600 |
Calculated Sample Size | 8.3576 |
Result | |
Sample Size Needed | 9.0000 |
the sample size necessary for a 95% confidence level with maximal margin of error E = 1.20 for the mean concentration of uric acid in this patient's blood is 9
Overproduction of uric acid in the body can be an indication of cell breakdown. This may...
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Overproduction of unic acid in the body can be an indication of cell break down. This may be an advance indication of its such as gout, leukemia, or lymphoma. Over a period of months and male patient has taken twelve blood tests for uric acid. The mean concentration was x 5.35 mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal with Said (a) Find a condence interval for the population mean concentration of...