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, 35New Diet: 47, 75, 85, 100, 58Let µnew and µold be the population mean milk productions for the new and old diets, respectively. She wishes to test: H0 : µnew vs µold = 0 vs. HA : µnew vs µold 6= 0, using α = 0.05.(a) Are the two populations paired or independent?

Answer:Step-by-step explanation: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 = 11Std dev for difference = 13.3689a) 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) Enclosedc) 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 alphaSo reject null hypothesis.The two means are statistically significantly different.