Question

For part a could you show me how using r code make the necessary graphs, and for part b show me the work for how to solve the problem. thank you

1. A dairy scientist is testing a new feed additive. She chooses 13 cows at random from a large population. She randomly assigns nold = 8 to the old diet and nnew = 5 to a new diet including the additive. The cows are housed in 13 widely separated pens. After two weeks, she milks each cow and records the milk produced in pounds: Old Diet: 43, 51, 44, 47, 38, 46, 40, 35 New Diet: 47, 75, 85, 100, 58 Let µnew and µold be the population mean milk productions for the new and old diets, respectively. She wishes to test H0 : µnew − µold = 0 against HA : µnew − µold 6= 0 using α = 0.05.

(a) Graph the data as you see fit. Why did you choose the graph(s) that you did and what does it (do they) tell you?

(b) Choose a test appropriate for the hypotheses and justify your choice based on your answer to part (a). Then perform the test by 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 you wish, to check your work). Finally, state your conclusion in the context of the problem.

Answer 1

(a) The data have been graphed as given below:
2 boxplots have been used to graph the New Diet and Old Diet data. Boxplot has been used in order to study the spread and the symmetry of the data in order to judge whether the data has sampled from a normal distribution. From the boxplots, we can observe that the data seem to have been sampled from 2 different normal populations.