ttest1samp

ttest1samp is a one-sample t-test function used to determine whether the mean of a sample differs from a specified population mean (mu0). It is a common tool in statistical analysis for testing hypotheses about a single group's average.

Inputs typically include the data x and the hypothesized mean mu0. Optional parameters may specify the direction of the alternative hypothesis (two-sided, greater than, or less than), the significance level alpha, and the dimension along which to operate when x is multi-dimensional. Some implementations also provide a confidence interval for the mean.

Outputs generally include h, the test decision indicator (1 if the null hypothesis is rejected at the chosen alpha, 0 otherwise); p, the p-value of the test; ci, a (1 - alpha) confidence interval for the mean; and stats, a structure containing the t-statistic (tstat) and the degrees of freedom (df).

Computation follows the standard one-sample t-test formula: t = (x_bar − mu0) / (s / sqrt(n)), where x_bar is the sample mean, s is the sample standard deviation, and n is the sample size. The degrees of freedom are df = n − 1, and the p-value is derived from the t-distribution according to the specified tail of the alternative hypothesis.

Assumptions center on independence of observations and approximate normality of the population, particularly for small samples. A small p-value indicates that the observed mean is unlikely under mu0, supporting a difference from mu0; a confidence interval that excludes mu0 aligns with rejecting the null hypothesis at the chosen significance level.

See also related one-sample testing methods in statistics for alternative approaches when normality or other assumptions are in question.