3. A dairy scientist is testing a new feed additive. She chooses 13 cows at rand

Question

3. 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 /= 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. Finally, state your conclusion in the context of the problem.

Explanation / Answer

here we cannot check that whether the data is pair wise related or not because the data on both Old Diet New Diet: is not of same length

c) H0 : µnew µold = 0 vs. HA : µnew µold /= 0, using = 0.05.

N Mean StDev SE Mean
C1 8 43.00 5.18 1.8
C2 5 73.0 21.1 9.4

Difference = mu (C1) - mu (C2)
Estimate for difference: -30.00
95% CI for difference: (-46.77, -13.23)
T-Test of difference = 0 (vs not =): T-Value = -3.94 P-Value = 0.002 DF = 11
Both use Pooled StDev = 13.3689

so we reject H0 as p-value < = 0.05

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