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UW-Madison STAT 371 - STAT 371 Discussion 7

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STAT371 DISCUSSION 7 October 19, 20021. Conditions for validity of estimation methods• Conditions regarding the design of the study– It must be reasonable to regard the data as a random samplefrom a large population.– The observations in the sample must be independent of eachother.• – If n is samll, the population distribution must be approxi-mately normal.– If n is large, the population distribution need not be appro-mately normal.The requirement that the data are a random sample is the mostimportant condition.2. Confidence interval for a population proportion• The 95% confidence interval for p is:˜p ± 1.96SE˜pwhere˜p =y + 2n + 4and standard error for ˜pisSE˜p=s˜p(1 − ˜p)n + 4• Planning a study to estimate pIf a desired value of SE˜pis specified, and if a rough informed guessof ˜p is available, than the require sample size n can be determinedfrom the following equation:Desired SE =s(Guessed˜p)(1 − Guessed˜p)n + 413. Comparison of two independent samples• Standard error of (¯y1− ¯y2) isSE(¯y1−¯y2)=ss21n1+s22n2=qSE21+ SE22whereSE1= SE¯y1=s1√n1and SE2= SE¯y2=s2√n2• The 100(1 − α)% confidence interval for µ1− µ2is constructed as(¯y1− ¯y2) ± tα2SE(¯y1−¯y2)The degree of freedom of Student’s t distribution isdf =(SE21+ SE22)2SE41(n1−1)+SE42(n2−1)where SE1=s1√n1and


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UW-Madison STAT 371 - STAT 371 Discussion 7

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