The liver is the main storage site of vitamin A and copper. Inverse relationships between copper and vitamin A liver concentrations have been suggested. In Rachman et al. (1987) the consequences of a copper-deficient diet on liver and blood vitamin A storage in Wistar rats was investigated. Nine animals were fed a copper-deficient diet for 45 days from weaning. Concentrations of vitamin A were determined by isocratic high-performance liquid chromatography using UV detection. Rachman et al. (1987) observed in the liver of the rats fed a copper-deficient diet a mean level of retinol, in micrograms/g of liver, was X = 4.3 and s = 0.9. It is known that the normal level of retinol in a rat liver is po = 1.3. (a) Find the 99% confidence interval for the mean level of liver retinol in the population of copper-deficient rats. (b) Test the hypothesis that the mean level of retinol in the population of copper-deficient rats is uo = 1.3 versus a sensible alternative, either one-sided or two-sided, at the significance level a = 0.05. Use both the rejection region and p-value approaches. (c) Calculate the power of the test in (b) against the alternative hypothesis Hi : M = M1 = 2.8? (d) Suppose that you are designing a new, larger study in which you are going to assume that the variance of observations is o2 = 1.53 , as the limited nine-animal study indicated. Find the sample size so that the power of rejecting Ho when an alternative Hi : M = 2.4 is true is 0.90. Use a = 0.05