T statistic uses sample variance (s2) and the z-score uses the population variance (o2)
Used to test hypotheses about an unknown population mean, u, when the value of o is unknown. The t statistic uses the estimated standard error in the denominator. t = M - u / sM
Complete set of t values computed for every possible random sample for a specific sample size (n) for a specific degrees of freedom (df). The t distrib. approximates the shape of a normal distrib., especially for large samples or samples from a normal pop. How well a t distribution approximates a normal distrib. depends on df. As the sample size increases, the df also increases, and better the t distrib. approximates the normal distrib.
The shape of the t distribution
Exact shape changes w/ df. T distribution tends to be flatter and more spreadout, where as normal z distrib. has more of a central peak.
Estimated standard error
(sM), used as an estimate of the real standard error, oM, when the value of o is unknown. Computed using sample variance or sa,ple standard dev & provides estimate of standard distance btwn a sample mean, M, & the population mean, u.