Horng-Chyi HorngStatistics II_Five43 Inference on the Variances of Two Normal Population &5-5 (&9-5)

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)


The Test ProcedureThe Test Procedure


Confidence Interval on the Ratio of Confidence Interval on the Ratio of Two VariancesTwo Variances


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


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


Inference on Two Population Inference on Two Population Proportions (III)Proportions (III)

21

21^

nn

XXPwhere


Confidence Interval for pConfidence Interval for p11 – p – p22

Horng-Chyi HorngStatistics II_Five43 Inference on the Variances of Two Normal Population &5-5 (&9-5)

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