ettprøvettest

ettprøvetest is a statistical method for evaluating a hypothesis about a population parameter using data from a single sample. In practice it is used to decide whether the parameter equals a specified value, such as the population mean or proportion. The term is commonly translated as "one-sample test" and encompasses several specific tests, including the one-sample t-test, the one-sample z-test, and the one-sample proportion test.

One-sample t-test: used when the population standard deviation is unknown and the data are approximately normally distributed. The test statistic is t = (x_bar - mu0) / (s / sqrt(n)). The null hypothesis H0: mu = mu0; the alternative depends on the research question. One-sample z-test: used when the population standard deviation sigma is known; Z = (x_bar - mu0) / (sigma / sqrt(n)); under H0, Z follows a standard normal distribution. One-sample proportion test: tests H0: p = p0; the test statistic Z = (phat - p0) / sqrt(p0(1-p0)/n), where phat is the sample proportion. Nonparametric alternatives exist for median or distribution-free contexts, such as the Wilcoxon signed-rank test.

Procedure: formulate H0 and H1, choose alpha, compute the test statistic from the sample, obtain a p-value or critical value, and decide whether to reject H0. Report the estimate of the parameter, the test statistic, the p-value, and a confidence interval when appropriate.

Assumptions: samples should be randomly drawn and independent. The t-test assumes approximate normality of the population or a sufficiently large sample; the z-test assumes known sigma. Proportion tests assume a large enough sample for the normal approximation, or use exact tests in small samples.

See also: t-test, z-test, hypothesis testing, Wilcoxon signed-rank test, confidence interval.