Final answer:
The statement is true; the mean of the sampling distribution of p-hat is equal to the population proportion p.
Step-by-step explanation:
True. The mean of the sampling distribution of p-hat, which is the sample proportion, is equal to the population proportion p. In statistics, this principle is related to the Central Limit Theorem, which states that as the sample size becomes larger, the sampling distribution of the sample means will tend to be normally distributed around the population mean. In the case of proportions, when the sample size is sufficiently large and the conditions for a binomial distribution are met (i.e., there are a number of independent trials, outcomes can be classified as success or failure, and each trial has the same probability of success p), then the sampling distribution of the sample proportion p-hat can also be approximated by a normal distribution with a mean of p and standard deviation √(p(1-p)/n), where n is the sample size.
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