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Horng-Chyi HorngHorng-Chyi Horng Statistics II_FiveStatistics II_Five 11
Inference on the Variances of Two Inference on the Variances of Two Normal PopulationNormal Population &5-5 (&9-5)
Horng-Chyi HorngHorng-Chyi Horng Statistics II_FiveStatistics II_Five 44
The Test ProcedureThe Test Procedure
Horng-Chyi HorngHorng-Chyi Horng Statistics II_FiveStatistics II_Five 88
Confidence Interval on the Ratio of Confidence Interval on the Ratio of Two VariancesTwo Variances
Horng-Chyi HorngHorng-Chyi Horng Statistics II_FiveStatistics II_Five 1010
Two independent random samples of size nTwo independent random samples of size n11 and n and n22 are are
taken from two populations, and let Xtaken from two populations, and let X11 and X and X22 represent represent
the number of observations that belong to the class of the number of observations that belong to the class of interest in samples 1 and 2, respectively.interest in samples 1 and 2, respectively.
For large samples, the estimation of the population For large samples, the estimation of the population proportions proportions
have approximate normal distributions.have approximate normal distributions.
Inference on Two Population Inference on Two Population Proportions (I)Proportions (I) &5-6 (&9-6)
222
^
111
^
/ and / nXPnXP
Horng-Chyi HorngHorng-Chyi Horng Statistics II_FiveStatistics II_Five 1111
Inference on Two Population Inference on Two Population Proportions (II)Proportions (II)
Therefore,Therefore,
is approximately standard normalization.is approximately standard normalization.
If HIf H00: p: p1 1 = p= p22 is true, that is, p is true, that is, p1 1 = p= p22 = p, then = p, then
)1,0(~
)11
)(1(21
2
^
1
^
N
nnpp
PPZ
Horng-Chyi HorngHorng-Chyi Horng Statistics II_FiveStatistics II_Five 1212
Inference on Two Population Inference on Two Population Proportions (III)Proportions (III)
21
21^
nn
XXPwhere
Horng-Chyi HorngHorng-Chyi Horng Statistics II_FiveStatistics II_Five 1515
Confidence Interval for pConfidence Interval for p11 – p – p22