Final answer:
The mean of the sampling proportion p' is the measure of central tendency for sample proportions and equals the true population proportion (p). It is relevant when dealing with categorical data outcomes, and the central limit theorem allows it to be normally distributed for large enough sample sizes.
Step-by-step explanation:
The mean of the sampling proportion, often represented as p', is a statistical measure that represents the central tendency of the sample proportions from multiple samples drawn from a population. The sample proportion is calculated by dividing the number of successes in the sample (x), by the total number of observations in the sample (n). According to the central limit theorem for proportions, the sampling distribution of the sample proportion approaches a normal distribution with a mean equal to the true population proportion (p) and a standard deviation equal to the square root of p(1-p)/n, where q is 1 minus the population proportion (p).
To be confident you are dealing with a proportion problem, look for scenarios where the data is categorical with two potential outcomes, like 'Success' or 'Failure', or 'Yes' or 'No'. Examples include estimating the proportion of the population that smokes, will vote for a certain candidate, or has a college-level education. When constructing confidence intervals for population proportions, the principles are similar to those used for population means, though the formulas differ slightly to accommodate the nature of proportion data.