What type of variable is required to construct a confidence interval for a population proportion?

Verified step by step guidance

1. Understand that a population proportion refers to the fraction or percentage of the population that has a particular characteristic or attribute.
2. Recognize that to construct a confidence interval for a population proportion, the variable of interest must be categorical, specifically a binary (dichotomous) variable.
3. A binary variable means it has only two possible outcomes, such as 'success' or 'failure', 'yes' or 'no', 'present' or 'absent'.
4. This binary nature allows us to count the number of successes in a sample and estimate the proportion of successes in the population.
5. Therefore, the variable required is a categorical variable with two categories, often called a Bernoulli or binomial variable.

Key Concepts

Population Proportion

A population proportion represents the fraction or percentage of individuals in a population that have a particular characteristic. It is a parameter often denoted by p and is estimated using sample data. Understanding this helps in constructing confidence intervals to estimate the true proportion.

Categorical (Qualitative) Variable

A categorical variable classifies data into distinct groups or categories, such as yes/no or success/failure. To construct a confidence interval for a population proportion, the variable must be categorical because proportions measure the relative frequency of categories.

Confidence Interval for a Proportion

A confidence interval for a population proportion estimates the range within which the true proportion lies with a certain level of confidence (e.g., 95%). It requires sample data from a categorical variable and uses formulas based on the sample proportion and sample size.