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handout_12 DISTRIBUTION OF THE SAMPLE PROPORTION

# handout_12 DISTRIBUTION OF THE SAMPLE PROPORTION - Apr 1510...

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Apr 15’10 DISTRIBUTION OF THE SAMPLE PROPORTION #12 Earlier in handouts #9, 10, 11 we considered the sampling distributions of the sample means and the difference between two sample means. Health workers are often interested, however, in the sampling distribution of a statistic, such as sample proportion , that results from counts or frequency data. The following example gives us some representation about one type of problems involving a sample proportion. Example 1 . Results from the 1999-2000 National Health and Nutrition Examination Survey, show that 31% of U.S. adults ages 20-74 are obese (obese as defined with body mass index greater than or equal to 30.0). We designate this population proportion as p = 0.31 . If we randomly select, say, 150 individuals from this population, what is the probability that the proportion in the sample who are obese will be greater than the value of 0 = 0.40 ? To answer this question we need to know the properties of the sampling distribution of the sample proportion . Below the sample proportion is designated as , and the population proportion is designated as p . Sampling distribution of  : Construction . The sampling distribution of a sample proportion would be constructed experimentally in exactly the same manner as was suggested in the case of arithmetic mean (see handout #9). From the population, which we assume to be finite, we would take all possible samples of a given size and for each of them compute the sample proportion,  . We would then prepare a frequency distribution of  by listing the different distinct values of  along with their frequencies of occurrence. This frequency distribution (as well as the corresponding relative frequency distribution) would constitute the sampling distribution of

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handout_12 DISTRIBUTION OF THE SAMPLE PROPORTION - Apr 1510...

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