The one-sample t statistic and Figure 1 Density curve for the t distributions with 2 and 9 degrees of freedom and the he t distributions standard normal distribution raw an SRS of size n from a population that has the normal distribution with meanu and standard deviation o the one- has the t distribution with n-1 degrees of freedom The t statistic has the same interpretation as any standard statistic: it says how farx The figure illustrates these facts is from its mean u in standard deviation about the t distributions The degrees of freedom for one-sample t The density curves of the t distributions statistic come from the sample standard are similar in shape to the standard normal deviation s in the denominator of t We know that s has n-1 degree of freedom We will write the t distribution with k degrees of freedom as t(k) for short9 17 The one-sample t statistic and the t distributions • Draw an SRS of size n from a population that has the normal distribution with mean and standard deviation . The one￾sample t statistic has the t distribution with n-1 degrees of freedom. x t s n − μ = μ σ 18 • The t statistic has the same interpretation as any standard statistic: it says how far is from its mean in standard deviation units. • The degrees of freedom for one-sample t statistic come from the sample standard deviation s in the denominator of t. We know that s has n-1 degree of freedom. We will write the t distribution with k degrees of freedom as t(k) for short. x μ 10 19 Figure 1 Density curve for the t distributions with 2 and 9 degrees of freedom and the standard normal distribution. 20 The figure illustrates these facts about the t distributions: • The density curves of the t distributions are similar in shape to the standard normal curve. They are symmetric about zero, single-peaked, and bell-shaped