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**STATISTICAL INFERENCE ABOUT MEANS AND PROPORTIONS WITH TWO POPULATIONS**

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**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

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**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)

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**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)

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Interval Estimate of the Difference Between the Means of Two Population: Large-Sample Case With and Estimated by and (10.6)

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**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)

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**Pooled estimator of (10.8) Point Estimate of When (10.9)**

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Interval Estimate of the Difference Between the Means of Two Populations: Small-Sample Case With and Estimated by and (10.10)

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**10.2HYPOTHESIS TESTS ABOUT THE DIFFERENCE BETWEEN THE MEANS OF TWO POPULATIONS :INDIFFERENT SAMPLE**

Large-sample Case (10.11)

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**Small-Sample Case (10.12) where**

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**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)

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**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)

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**Sampling Distribution of**

Expected Value: (10.15) Standard deviation: (10.16)

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**Interval Estimation of**

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

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**Hypothesis Tests About**

(10.19) (10.20) (10.21)

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