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Suppose we want to test the hypothesis that people using a new dose A of ampicillin have different urine concentration (g/mL) to that of standard dose B. We recruit 169 volunteers who have received dose A of ampicillin and find they have a mean concentration of 7.5 g/mL with a standard deviation of 3.5 g/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 standard deviation of the concentrations.

c) How large a sample would be needed to ensure that the length of the CI in problem Q(a) is less than 0.7 g/mL assuming the sample standard deviation remains at 3.5 g/mL?