Suppose we want to estimate the concentration (ug/mL) of a specific does of ampicillin in the urine after various periods of time. We recruit 25 volunteers who have received ampicillin and find they had a mean concentration of 7.0 ug/mL with a standard deviation of 2.0 ug/mL. Assume the underlying population distribution of concentrations is normally distributed.
1) Find a 95 percent CI for the population mean concentration.
2) Find a 99 percent CI for the population variance of the concentrations.
3) How large a sample would be needed to ensure that the length of the confidence interval in 1) is 0.5 ug/mL if we assume the sample standard deviation remains at 2.0 ug/mL?