The t confidence intervals and tests To test the hypothesis Ho A=u based on an SRS of size n, compute the To analyze samples from normal one-sample t statistic populations with unknown o, just replace the standard deviationa/n of x by its standard error in the z procedures The z procedures then become one- mple t procedures. Use P-value or critical values from the t distribution with n- 1 degrees of freedom in place of the normal values The one-sample t procedures In terms of a variable T having t(n distribution, the P-value for a test of Ho Draw an SRS of size n from a population against having unknown mean u. Alevel C confidence interval for p is H1:x>isP(T≥1) x±t H1;<AisP(T≤ where t is the upper(1-c)/2 critical value H1:≠6 for the t(n-1)distribution13 25 The t confidence intervals and tests • To analyze samples from normal populations with unknown , just replace the standard deviation of by its standard error in the z procedures. The z procedures then become one￾sample t procedures. Use P-value or critical values from the t distribution with n- 1 degrees of freedom in place of the normal values. σ σ n x s n 26 The one-sample t procedures • Draw an SRS of size n from a population having unknown mean . A level C confidence interval for is μ s x t n ± where t is the upper (1-C)/2 critical value for the t(n-1) distribution. μ 14 27 • To test the hypothesis based on an SRS of size n, compute the one-sample t statistic 0 0 H : μ = μ 0 x t s n − μ = 28 • In terms of a variable T having t(n-1) distribution, the P-value for a test of against H0 1 0 H PT t : is ( ) μ > ≥ μ 1 0 H : is ( ) μ < ≤ μ PT t 1 0 H PT t : is 2 ( ) μ μ ≠ ≥