A researcher wants to conduct a randomized experiment to examine the effect of LSD on concentrations of chemical norepinephrine (NE) in the medulla region of the brain in rats. Half of the rats available for the study will be randomly assigned to a control group and the other half will be ex-posed to a specific amount of LSD. Information from other studies suggests the mean concentrationof NE brain tissue of normal rats, not exposed to LSD, is about 450 ng/gm, and the populationstandard deviation is about 70 ng/gm. The researcher has decided that it would important todetect if exposure to the amount of LSD used in the study causes either a 10% increase or a 10%decrease in NE concentration. Using a Type I error level of 0.05, the researcher wants power 0.80of detecting an effect of this magnitude.(a) Determine how many rats the researcher needs to have in each group.(b) If the researcher suspected that LSD tends to increase NE concentration and planned to usea one-tailed t-test, what would be the required number of rats?(c) Suppose that by switching to a better supplier of rats and improving lab procedures, theresearcher could cut the population standard deviation in half, but these improvements woulddouble the cost of each observation. Would these measures be cost effective?