Hypotheseproportie

Hypotheseproportie is a term used in statistics to denote a hypothesis about the proportion of a binary outcome in a population. It is addressed in hypothesis testing to determine whether the true population proportion p matches a specified value p0 or deviates from it. The concept is applicable across disciplines such as medicine, social sciences, quality control, and market research.

Typically, the null hypothesis is H0: p = p0, with an alternative H1: p ≠ p0 (two-sided) or one-sided variants like H1: p > p0 or p < p0. The sample statistic is the sample proportion phat = x/n, where x is the number of successes in a sample of size n. For large samples, a common test statistic is Z = (phat − p0) / sqrt[p0(1 − p0)/n], which under H0 is approximately standard normal. For small samples, an exact binomial test is preferred.

The testing process involves collecting a random sample, calculating phat, selecting a significance level alpha, computing a p-value, and deciding whether to reject H0. Confidence intervals for p, such as Wilson or Clopper–Pearson intervals, can be obtained by inverting the corresponding tests. Power analysis and sample size calculations are also used to plan studies intended to detect specified differences in proportion.

Assumptions for valid inference include random sampling, independence of observations, and a binary outcome. Limitations arise when the normal approximation is inadequate, such as with very small samples or extreme p values; in such cases, exact methods or alternative approaches are recommended.