A dairy scientist is testing a new feed additive. She chooses 13cows at random from a large population. She randomly assigns n_old= 8 to the old diet and n_new = 5 to a new diet including theadditive. The cows are housed in 13 widely separated pens. Aftertwo weeks, she milks each cow and records the milk produced inpounds:
Old Diet: 43, 51, 44, 47, 38, 46, 40, 35 New Diet: 47, 75, 85,100, 58
Let ?new and ?old be the population mean milk productions forthe new and old diets, respectively. She wishes to test H0 : ?new ??old = 0 against HA : ?new ? ?old ?= 0 using ? = 0.05.
(a) Graph the data as you see fit. Why did you choose thegraph(s) that you did and what does it (do they) tell you?
(b) Choose a test appropriate for the hypotheses and justifyyour choice based on your answer to part (a). Then perform the testby computing a p-value, and making a reject or not reject decision.Do this without R and show your work. (Also do it with R, if youwish, to check your work). Finally, state your conclusion in thecontext of the problem.
