An experiment was designed to estimate the mean difference in weight gain for pi
ID: 3132743 • 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 90% 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 51 56 60 48 44 57 51 Ration B 55 42 46 54 38 39 49 41Explanation / Answer
Here we have mean for A as 53.5 and sd as 5.98 for B we have mean is 45.5 and sd as 6.61
Since we are trying to estimate the difference between population means, we choose the difference between sample means as the sample statistic. Thus, x1bar -x2bar=8
SE = sqrt [ s21 / n1 + s22 / n2 ]
SE = sqrt [(5.98)2 / 8+ (6.61)2 / 8]
SE = 3.15
DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }
DF = 13.78
Therefore, the 90% confidence interval is 8+-5.55; that is, 2.45 to 13.55. Here's how to interpret this confidence interval. Based on the confidence interval, we would expect the observed difference in sample means to be between 2.45 to 13.55
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