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handout_13 DISTRIBUTION OF THE DIFFERENCE BETWEEN TWO SAMPLE PROPORTIONS

# Handout_13 DISTRIBUTION OF THE DIFFERENCE BETWEEN TWO SAMPLE PROPORTIONS

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Apr 19’09 DISTRIBUTION OF THE DIFFERENCE BETWEEN TWO #13 SAMPLE PROPORTIONS. CONFIDENCE INTERVAL. Often researchers are interested in the probability associated with a difference 1 2 between proportions 1 and 2 computed from samples drawn from two populations. The relevant sampling distribution is the distribution of the difference between the two sample proportions. Sampling distribution of 1 2 : Construction . The sampling distribution of a difference between two sample proportions would be constructed experimentally in exactly the same manner as was suggested in the case of the difference between two means (see handouts #9 - 11). Given two sufficiently small populations, one would draw, from population 1, all possible simple random samples of size n 1 and compute, from each set of sample data, the sample proportion 1 . From population 2, one would draw independently all possible simple random samples of size n 2 and compute, from each set of sample data, the sample proportion 2 . Then one would compute the differences between all possible pairs of sample proportions, where one number of each pair was a value of 1 and the other of value of 2 . At last, one would prepare a frequency distribution of differences  1 2  by listing the different distinct values of 1 2 along with their frequencies of occurrence. This frequency distribution (as well as the corresponding relative frequency distribution) would constitute the sampling distribution of 1 2 . Sampling distribution of 1 2 : Characteristics . The characteristics of the sampling distribution in question are as follows. Let us assume that we deal with two populations of dichotomous variables which may take one of two possible mutually exclusive values. If independent random samples of size n 1 and n 2

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