3.4/ THE t DISTRIBUTION 1. Definition If we draw random samples from a normal population with mean u and variance o2 but replaced by its estimator $2, the sample mean follows the t distribution. X-4 S/√n 2. Properties of the t distribution The t distribution is symmetric; The mean of the t distribution is zero but its variance is k/(k-2). The t distribution is flatter than the normal distribution The t distribution, like the chi-square distribution approaches the standard normal distribution as the d.f. Increase3.4 THE t DISTRIBUTION 1. Definition If we draw random samples from a normal population with mean μ and variance σ2 but replaceσ2 by its estimator S2 , the sample mean follows the t distribution. 2. Properties of the t distribution The t distribution is symmetric; The mean of the t distribution is zero but its variance is k/(k-2). The t distribution is flatter than the normal distribution. The t distribution, like the chi-square distribution, approaches the standard normal distribution as the d.f. increase. S n X t / −  =