Which type of variable is required to construct a confidence interval for a $p$ (population proportion)?

• A. A categorical variable with two possible outcomes ($\mathrm{binary}$ variable)
• B. A continuous variable measured on an interval or ratio scale
• C. A discrete variable with more than two categories
• D. A qualitative variable with no defined categories

Answer: (A)

Verified step by step guidance

1. Understand that a confidence interval for a population proportion estimates the true proportion of a specific category or outcome in the population.
2. Recall that proportions are calculated from categorical data, where each observation falls into one of several categories.
3. Recognize that to construct a confidence interval for a population proportion, the variable must be categorical with exactly two possible outcomes (binary), such as success/failure or yes/no.
4. Note that continuous variables or categorical variables with more than two categories are not suitable for this type of confidence interval because proportions are defined for binary outcomes.
5. Therefore, the required variable type is a categorical variable with two possible outcomes (a binary variable).