The following are some of the data collected in one of the mensuration exercises
ID: 3243764 • Letter: T
Question
The following are some of the data collected in one of the mensuration exercises. The measurements are volumes in m3/ha for 24 different plots:
Column 1
Column 2
736
1009
1560
1413
990
1528
924
1079
1042
1207
1360
1770
936
826
1618
1573
1221
1259
1033
1564
1288
896
555
1462
a) Assume that each column of data comes from a different forest type. Is it very likely to get a variance ratio S12/S22 as big as, or greater than what you got if you assume that 12 = 22 . Can you assume that 12 = 22 with a good probability?
b)You don't know the population variance of the two forest types, but you are told that µ1 = µ2 . What is the probability that, if you take 12 plots from each type:
i)x2 - x1 200?
ii) 100 x2 - x1 200?
iii) to get a difference as big as you have or greater?
Column 1
Column 2
736
1009
1560
1413
990
1528
924
1079
1042
1207
1360
1770
936
826
1618
1573
1221
1259
1033
1564
1288
896
555
1462
Explanation / Answer
ans=
Mean(F1) = (736+1560+990+924+1042+1360+936+1618+122... )= 1,105.25
S^2(F1) = (736^2+1560^2+990^2+924^2+1042^2+1360^2+... )= 10,0411.3
Mean(F2) = (1009+1413+1528+1079+1207+1770+826+1573+...) = 1298.83
S^2(F2) = (1009^2+1413^2+1528^2+1079^2+1207^2+1770... )= 91230.59
a)
H0: ^2(1) = ^2(2)
H1: ^2(1) > ^2(2), = 0.05
Decision Rule:
If S^2(F1)/S^2(F2) > F(n1 - 1, n2 - 1; 1 - ), we reject H0.
If 100411.3/91230.59 > F(11, 11; 0.95), we reject H0.
If 1.1 3.44, we don't Reject H0
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