A dairy scientist is testing a new feed additive. She chooses 13 cows at random from a large population of cows. She randomly assigns nold = 8 to get the old diet, and nnew = 5 to get the new diet including the additive. The cows are housed in 13 separated pens and each gets separate feed, with or without additive as appropriate. After two weeks, she picks a day and milks each cow using standard procedures and records the milk produced in pounds. The data are below:

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 vs. HA : µnew ? µold 6= 0, using ? = 0.05.

(a) Are the two populations paired or independent? Explain your answer.

(b) 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?

(c) Choose a test appropriate for the hypotheses above, and justify your choice based on your answers to parts (a) and (b). Then perform the test by computing a p-value, and making a reject or not reject decision. Do not use R for this, and show your work. Finally, state your conclusion in the context of the problem.

Given that a dairy scientist is testing a new feed additive. She chooses 13 cows at random from a large population of cows. She randomly assigns nold = 8 to get the old diet, and nnew = 5 to get the new diet including the additive.

From the data given we get the following

N Mean StDev SE Mean

Sample 1 8 43 5.1824 1.832

Sample 2 5 73 21.0832 9.429

df = 11

Std dev for difference = 13.3689

a) Yes the two are independent. The two sets of cows randomly chosen are definitely independent. Paired means equal number should be there and homogeneous conditions should be maintained.

b) Enclosed

c) Comparison of two means is the test recommended here. Because independent samples are used.\

d) Test statistic= -3.1233

(because of unequal variances we use that method)

95% confidence interval = ( -56.6676 , -3.3324 )

p value <0.05 our alpha

So reject null hypothesis.

The two means are statistically significantly different.