Final answer:
B) P cap is the sample proportion, and P hat is the population proportion is the correct answer. P cap, denoted as p′, represents the sample proportion, while P hat represents the true population proportion, which the sample proportion is used to estimate. Option B is correct.
Step-by-step explanation:
The question deals with the concepts of population and sample proportions in statistics, which are represented by symbols P cap and P hat. The correct option is B) P cap is the sample proportion, and P hat is the population proportion.
This can cause confusion because P cap, denoted as p′, is indeed the symbol for the sample proportion and serves as the point estimate for the true population proportion. It is calculated using the formula p′ = x/n, where x represents the number of successes in the sample, and n is the sample size.
The sample proportion, P cap (or p′), is calculated from data collected from a sample and is used to estimate the true population proportion, which is denoted by P hat (or p). When we discuss population proportion, we're referring to the true proportion of individuals or items in a complete population that meet a certain criterion.
In hypothesis testing, one might compare two different sample proportions to infer if there are differences in the actual population proportions based on the collected sample data. A commonly used test is the two independent sample proportions test, which can be used to determine if there's a significant difference between two population proportions.