An experiment was designed to estimate the mean difference in weight gain for pi
ID: 3134763 • Letter: A
Question
An experiment was designed to estimate the mean difference in weight gain for pigs fed ration A as compared with those fed ration B. Eight pairs of pigs were used. The pigs within each pair were litter-mates. The rations were assigned at random to the two animals within each pair. The gains (in pounds) after 45 days are shown in the following table. Assuming weight gain is normal, find the 95% confidence interval estimate for the mean of the differences d, where d = ration A - ration B. (Give your answers correct to two decimal places.)
Litter 1 2 3 4 5 6 7 8 Ration A 61 49 64 51 39 48 48 49 Ration B 51 43 57 49 37 42 46 46Explanation / Answer
10
6
7
2
2
6
2
3
The differences are
Calculating the standard deviation of the differences (third column):
s = 3.325748947
Thus, the standard error of the difference is sD = s/sqrt(n):
sD = 1.175829817
Calculating the mean of the differences (third column):
XD = 4.75
For the 0.95 confidence level,
alpha/2 = (1 - confidence level)/2 = 0.025
t(alpha/2) = 2.364624252
lower bound = XD - t(alpha/2) * sD = 1.9696043
upper bound = XD + t(alpha/2) * sD = 7.5303957
Thus, the confidence interval is
( 1.9696043 , 7.5303957 ) [ANSWER]
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