Suppose we want to estimate the concentration (µg/mL) of a specific dose of ampicillin in the urine after various periods of time. We recruit 25 volunteers who have received ampicillin and find they have a mean concentration of 7.0 µg/mL with a standard deviation of 2.0 µg/mL. Assume the underlying population distribution of concentrations is normally distributed. A) Find a 95% CI for the population mean concentration. B) Find a 99% CI for the population variance of the concentrations. C) How large a sample would be needed to ensure that the length of the CI in Problem 6.30 is 0.5 µg/mL assuming the sample standard deviation remains at 2.0 µg/mL?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Suppose we want to estimate the concentration (µg/mL) of a specific dose of ampicillin in the urine after various periods of time. We recruit 25 volunteers who have received ampicillin and find they have a mean concentration of 7.0
µg/mL with a standard deviation of 2.0 µg/mL. Assume the underlying population distribution of concentrations is
A) Find a 95% CI for the population mean concentration.
B) Find a 99% CI for the population variance of the concentrations.
C) How large a sample would be needed to ensure that the length of the CI in Problem 6.30 is 0.5 µg/mL assuming the sample standard deviation remains at 2.0 µg/mL?
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