Definition: The Sampling Distribution of Proportion measures the proportion of success, i.e. a chance of occurrence of certain events, by dividing the number of successes i.e. chances by the sample size ’n�. Thus, the sample proportion is defined as p = x/n.
The sampling distribution of proportion obeys the binomial probability law if the random sample of ‘nâ€� is obtained with replacement. Such as, if the population is infinite and the probability of occurrence of an event is â€�Ï€â€�, then the probability of non-occurrence of the event is (1-Ï€).  Now consider all the possible sample size ‘nâ€� drawn from the population and estimate the proportion ‘pâ€� of success for each. Then the mean (?p) and the standard deviation (σ±è) of the sampling distribution of proportion can be obtained as:
?p = mean of proportion
π = population proportion which is defined as π = X/N, where X is the number of elements that possess a certain characteristic and N is the total number of items in the population.
σ±è = standard error of proportion that measures the success (chance) variations of sample proportions from sample to sample
n= sample size, If the sample size is large (n�30), then the sampling distribution of proportion is likely to be normally distributed.
The following formula is used when population is finite, and the sampling is made without the replacement:
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