# STATISTICAL INFERENCE ABOUT MEANS AND PROPORTIONS WITH TWO POPULATIONS

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STATISTICAL INFERENCE ABOUT MEANS AND PROPORTIONS WITH TWO POPULATIONS

STATISTICS IN PRACTICE
The testing process in the pharmaceutical industry usually consists of three stages : 1.preclinical testing 2.testing for long-term usage and safety 3.clinical efficacy testing

10.1 ESTIMATION OF THE DIFFERENCE BETWEEN THE MEANS OF TWO POPULATINS:INDEPENDENT SAMPLES
Point Estimator of the Difference Between the Means of populations (10.1) Sampling Distribution of Expected Distribution of (10.2) (10.3)

Interval Estimate of :large-sample case
Interval Estimate of the Difference Between the Means of Two Populations: Large-Sample Case (10.4) Point Estimator of (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
We begin by making the following assumption: 1.Both populations have normal distributions 2.The variances of the populations are equal (10.7)

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)

10.2HYPOTHESIS TESTS ABOUT THE DIFFERENCE BETWEEN THE MEANS OF TWO POPULATIONS :INDIFFERENT SAMPLE
Large-sample Case (10.11)

Small-Sample Case (10.12) where

10.3 INFERENCES ABOUT THE DIFFERENCE BETWEEN THE MEANS OF TWO POPULATIONS:MATCHD SAMPLE
In choosing the sampling procedure that will be used to collect production time data and test the hypotheses ,we consider two alternative designs: 1.Independent sample design 2.Matched sample design (10.13)

10.4 INFERENCES ABOUT THE DIFFERENCE BETWEEN THE PROPORTIONS OF TWO POPULATIONS
Point Estimator of the difference Between the Proportions of Two Populations (10.14)

Sampling Distribution of
Expected Value: (10.15) Standard deviation: (10.16)

Interval Estimation of
Point Estimator of (10.17) Interval Estimate of the Difference Between the Two Populations: Large-Sample Case With (10.18)