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In statistics, a population proportion refers to the fraction of individuals in a population with a certain characteristic. For example, suppose 43.8% of individuals in a certain city support a new law. The value 0.438 represents a population proportion.
In statistics a population proportion, generally denoted by or the Greek letter, [1] is a parameter that describes a percentage value associated with a population. A census can be conducted to determine the actual value of a population parameter, but often a census is not practical due to its costs and time consumption.
What is the Population Proportion? A population proportion is a fraction of the population that has a certain characteristic. For example, let’s say you had 1,000 people in the population and 237 of those people have blue eyes.
If X is a binomial random variable, then X ~ B (n, p) where n is the number of trials and p is the probability of a success. To form a proportion, take X, the random variable for the number of successes and divide it by n, the number of trials (or the sample size).
The procedure to find the confidence interval, the sample size, the error bound for a population (EBP), and the confidence level for a proportion is similar to that for the population mean, but the formulas are different.
The population proportion is denoted \(p\) and the sample proportion is denoted \(\hat{p}\). Thus if in reality \(43\%\) of people entering a store make a purchase before leaving, \[p = 0.43 \nonumber \]
In statistics, a population proportion refers to the fraction of individuals in a population with a certain characteristic. For example, suppose 43.8% of individuals in a certain city support a new law. The value 0.438 represents a population proportion.
The population proportion [latex]p = \frac{\text{# of individuals having a certain attribute}}{\text{population size}} = \frac{\text{# of successes}}{N}[/latex] is another parameter used to describe the population.
X ∼ B(n, p) where n is the number of trials and p is the probability of a success. To form a proportion, take X, the random variable for the number of successes and divide it by n, the number of trials (or the sample size). The random variable ˆp (read "p hat") is that proportion, ˆp = X n.
A population proportion is the share of a population that belongs to a particular category. Confidence intervals are used to estimate population proportions.