# Chapter10 STATISTICAL INFERENCE ABOUT MEANS AND

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```					STATISTICAL INFERENCE ABOUT
MEANS AND PROPORTIONS WITH
TWO POPULATIONS
STATISTICS IN PRACTICE
w The testing process in the pharmaceutical industry
usually consists of three stages :
w 1.preclinical testing
w 2.testing for long-term usage and safety
w 3.clinical efficacy testing
10.1 ESTIMATION OF THE DIFFERENCE
BETWEEN THE MEANS OF TWO
POPULATINS:INDEPENDENT SAMPLES
w Point Estimator of the Difference Between the
Means of populations
w                    (10.1)
w Sampling Distribution of
w Expected Distribution of
w                     (10.2)

w                              (10.3)
Interval Estimate of             :large-sample case
w Interval Estimate of the Difference Between the Means of
Two Populations: Large-Sample Case
w                         (10.4)

w Point Estimator of

w                              (10.5)
Interval Estimate of the Difference Between
the Means of Two Population: Large-Sample
Case            With and Estimated by
and

(10.6)
Interval Estimate of               :Small-Sample Case

w We begin by making the following assumption:
w   1.Both populations have normal distributions
w   2.The variances of the populations are equal

w                                                  (10.7)
w
Pooled estimator of

(10.8)

Point Estimate of      When

(10.9)
Interval Estimate of the Difference
Between the Means of Two Populations:
Small-Sample Case
With and Estimated by and

(10.10)
DIFFERENCE BETWEEN THE MEANS OF
TWO POPULATIONS :INDIFFERENT
SAMPLE
w Large-sample Case

w                  (10.11)
Small-Sample Case

(10.12)

where
DIFFERENCE BETWEEN THE MEANS OF
TWO POPULATIONS:MATCHD SAMPLE
w In choosing the sampling procedure that
will be used to collect production time data
and test the hypotheses ,we consider two
alternative designs:
w 1.Independent sample design
w 2.Matched sample design
w                      (10.13)
DIFFERENCE BETWEEN THE
PROPORTIONS OF TWO POPULATIONS
w Point Estimator of the difference Between
the Proportions of Two Populations

w                    (10.14)
Sampling Distribution of

w Expected Value:                 (10.15)

w Standard deviation:

(10.16)
Interval Estimation of

w Point Estimator of

w                           (10.17)

w Interval Estimate of the Difference Between
the Two Populations: Large-Sample Case
With
w                       (10.18)

w                 (10.19)

w                 (10.20)

w                 (10.21)

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