A study was designed to estimate the true mean amount (u) of radioactive element in lichen. specimens. A random sample of 9 lichen specimens were investigated, leading to a sample mean and standard deviation being 0.009 and 0.005 microcurie per milliliter, respectively.
a. Construct a 99% confidence interval for u based on the sample.
b. Suppose the researchers want to increase the sampel size in order to estimate the mean to within 0.001 microcurie per milliliter of its true vale using a 99% confidence interval. Find the minimum sample size required to complete the research goal.
c. What assumption(s) do you need for your inference in (b)?