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Unformatted text preview: Probability and Statistics in the Life Sciences (Spring 2010) AMS 110.02 Lecture 7 (chap5&6) Donghyung Lee Section 5.2 Dichotomous Observations Population proportion and sample proportion : : ? P the population proportion of one category P the sample proprotion of one category How can we construct the sampling distribution of p Section 5.2 Dichotomous Observations Example (Superior Vision p152) , 30% " " , 20 /15 . In a certain human population of the individuals have superior distance vision in the sense of scoring or better on a standardized vision test without glasses If we were to examine a random sample of two persons from the popul . ! ation Construct the sampling distribution of p Y Pr obabi l i t y 1 0. 5 2 1 p 2 2 (.3) (.7) .49 C = 1 1 2 1 (.3) (.7) .42 C = 2 2 2 (.3) (.7) .09 C = Section 5.2 Dichotomous Observations Example (Superior Vision p152) 20, If we increase sample size into p p Y Pr obabi l i t y Y Pr obabi l i t y . 00 . 001 11 . 55 . 012 1 . 05 . 007 12 . 60 . 004 2 . 10 . 028 13 . 65 . 001 3 . 15 . 072 14 . 70 . 000 4 . 20 . 130 15 . 75 . 000 5 . 25 . 179 16 . 80 . 000 6 . 30 . 192 17 . 85 . 000 7 . 35 . 164 18 . 90 . 000 8 . 40 . 114 19 . 95 . 000 9 . 45 . 065 20 1. 00 . 000 10 . 50 . 031 Section 5.2 Dichotomous Observations Example (Superior Vision p152) Section 5.2 Dichotomous Observations Example (Superior Vision p152) 1. ( 35) ? 2. ( .50) ? 3. (.25 .35) ? 4. (.55 .65) ? P p P p P p P p = = = = = = Section 5.2 Dichotomous Observations Dependence on Sample Size Section 4.5 The Continuity Correction The Continuity Correction , . In many cases in real problems we use a normal curve to describe approximately the distribution of a discrete variable Often the disceteness of the variable can be ignored without introducing any serious error but for greater accuracy w . . e can take account of discreteness by applying a correction Continuity Correction = Section 4.5 The Continuity Correction The Continuity Correction ( ) The distribution of litter size defined as the number of live young in the first litter for a population of female mice Section 4.5 The Continuity Correction The Continuity Correction 7.8 2.3, . A normal curve with and superimposed on the litter size distribution the normal curve fits the distribution quite well = = = Section 4.5 The Continuity Correction The Continuity Correction ( ) 5 10. ( ) (5 10) 8.0 13.0 15.5 17.8 15.0 11.5 80.8% .808 ( ) . 5 7.8 10 7.8 (5 10) ( ) 2.3 2.3 a Find the percentage of litters with sizes between and use histogram P Y b Find the corresponding area under the normal curve Y P Y P P = + + + + + = = = ( 1.22 .96) .8315 .1112 .7203 ( .808) 5 10....
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 Spring '08
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