STAT371 DISCUSSION 7 October 19 2002 1 Conditions for validity of estimation methods Conditions regarding the design of the study It must be reasonable to regard the data as a random sample from a large population The observations in the sample must be independent of each other If n is samll the population distribution must be approximately normal If n is large the population distribution need not be appromately normal The requirement that the data are a random sample is the most important condition 2 Confidence interval for a population proportion The 95 confidence interval for p is p 1 96SEp where p y 2 n 4 and standard error for p is SEp s p 1 p n 4 Planning a study to estimate p If a desired value of SEp is specified and if a rough informed guess of p is available than the require sample size n can be determined from the following equation Desired SE s Guessedp 1 Guessedp n 4 1 3 Comparison of two independent samples Standard error of y 1 y 2 is SE y 1 y 2 whereSE1 SEy 1 s1 n1 s q s2 s21 2 SE21 SE22 n1 n2 and SE2 SEy 2 s2 n2 The 100 1 confidence interval for 1 2 is constructed as y 1 y 2 t 2 SE y 1 y 2 The degree of freedom of Student s t distribution is df SE21 SE22 2 SE41 SE42 n1 1 where SE1 s1 n1 and SE2 2 s2 n2 n2 1
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