Proportion

Definition

Proportion is the fraction of the total that possesses a certain attribute. It is calculated by dividing the number of elements with the attribute by the total number of elements.

5 Must Know Facts For Your Next Test

1. A proportion is expressed as a decimal or a percentage.
2. The sample proportion is denoted by $\hat{p}$ and is used to estimate the population proportion, denoted by $p$.
3. Proportions are used in constructing confidence intervals for population parameters.
4. In hypothesis testing, proportions play a key role, especially in tests about population means and differences between populations.
5. The central limit theorem applies to sample proportions, enabling normal approximation when sample size is large enough.

Review Questions

• What symbols are used to denote sample proportion and population proportion?
• How do you calculate the proportion from a given dataset?
• Why is the central limit theorem important when dealing with proportions?

Related terms

Sample Proportion:

$\hat{p}$ represents the fraction of sampled elements that possess a certain attribute.

Population Proportion:

$p$ represents the true fraction of all elements in a population that possess a certain attribute.

Confidence Interval:

A range of values derived from sample statistics that likely contains the value of an unknown population parameter.