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notes 24 - is about normal with mean of p and standard...

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Sampling Distributions for Sample Proportion, p-hat Submitted by gfj100 on Wed, 11/11/2009 - 11:59 If numerous repetitions of samples are taken, the distribution of is said to approximate a normal curve distribution. Alternatively, this can be assumed if BOTH n *p and n *(1 - p) are at least 10. [ SPECIAL NOTE: Some textbooks use 15 instead of 10 believing that 10 is to liberal. We will use 10 for our discussions.] Using this, we can estimate the true population proportion, p, by and the true standard deviation of p by s.e.( ) = , where s.e.( ) is interpreted as the standard error of Probabilities about the number X of successes in a binomial situation are the same as probabilities about corresponding proportions. In general, if np >= 10 and n (1- p ) >= 10, the sampling distribution of
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Unformatted text preview: is about normal with mean of p and standard error SE( ) = . Example. Suppose the proportion of all college students who have used marijuana in the past 6 months is p = .40. For a class of size N = 200, representative of all college students on use of marijuana, what is the chance that the proportion of students who have used mj in the past 6 months is less than .32 (or 32%)? Solution. The mean of the sample proportion is p and the standard error of is SE( ) = . For this marijuana example, we are given that p = .4. We then determine SE( ) = = = = 0.0346 So, the sample proportion is about normal with mean p = .40 and SE( ) = 0.0346. The z-score for .32 is z = (.32 - .40) / 0.0346 = -2.31. Then using Standard Normal Table Prob( < .32) = Prob(Z <. -2.31) = 0.0104....
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