CI for Proportions

Statistics · Axiom Academy

Constructing confidence intervals for population proportions We start by collecting a random sample from our population and calculating the sample proportion (denoted as p-hat or p̂). The sample proportion represents the fraction of successes in our sample: For example, if we survey 200 people and 120 prefer product A, then p̂ = 120/200 = 0.60 or 60%. 2. Confidence Interval Formula To construct a confidence interval for the population proportion, we use the following formula: z* = critical value from the standard normal distribution (e.g., 1.96 for 95% confidence) The term √(p̂(1-p̂)/n) is called the standard error of the sample proportion. 3. Conditions for Valid Inference Before using this confidence interval formula, we must verify that certain conditions are met: When these conditions are satisfied, the sampling distribution of p̂ is approximately normal, allowing us to use the z-interval formula.

This is the written version of the interactive lesson above. See the full Statistics course.