Final answer:
The statement is completely true, a sampling distribution of the proportion is a probability distribution of sample proportions. It follows a normal distribution by the central limit theorem for proportions, provided certain conditions are met.
Step-by-step explanation:
True. A sampling distribution of the proportion is indeed a probability distribution whose values are the sample proportions. When dealing with sampling distributions given simple random samples of size n from a population, the probability distribution of all the measured characteristics, such as the mean, proportion, or standard deviation for each sample, is referred to as a sampling distribution.
You know you are dealing with a proportion problem when the data you are collecting is categorical, with two possible outcomes often referred to as Success or Failure. For example, estimating the proportion of the population that smokes, that will vote for a specific candidate, or that has a college-level education are all cases where one is dealing with population proportions.
The distribution of the sample proportions is denoted by P' ("P prime") and, according to the central limit theorem for proportions, it follows a normal distribution with mean value p (the population proportion) and a standard deviation calculated using the formula \(\frac{\sqrt{p\cdot q}}{\sqrt{n}}\), where q = 1 - p. Here the conditions for using the normal approximation are that np and nq should both be greater than five (np > 5 and nq > 5).