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STATISTICAL INFERENCE ABOUT MEANS AND PROPORTIONS WITH TWO POPULATIONS.

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Presentation on theme: "STATISTICAL INFERENCE ABOUT MEANS AND PROPORTIONS WITH TWO POPULATIONS."— Presentation transcript:

1 STATISTICAL INFERENCE ABOUT MEANS AND PROPORTIONS WITH TWO POPULATIONS

2 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

3 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)

4 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)

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

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) 

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

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

9 10.2HYPOTHESIS TESTS ABOUT THE DIFFERENCE BETWEEN THE MEANS OF TWO POPULATIONS :INDIFFERENT SAMPLE  Large-sample Case  (10.11)

10 Small-Sample Case (10.12) where

11 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)

12 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)

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

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

15 Hypothesis Tests About  (10.19)  (10.20)  (10.21)


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