Statistical Formulas for Hypothesis Testing and Confidence Intervals, Study notes of Statistics

Download Statistical Formulas for Hypothesis Testing and Confidence Intervals and more Study notes Statistics in PDF only on Docsity! Formulas Use when σ is known. Single population under study. 0 0:H µ µ= 0x -z n µ σ= n z x * σ± 2 m zn      = σ Single z- test. Single confidence interval. Use when σ is known. Two populations under study 0 1:H 2µ µ= 2 2 2 1 2 1 21 nn xx z σσ + − = 2 2 2 1 2 1* 21 nn )xx( σσ +±− z . Two sample z-test. Two sample z confidence interval. Use when σ is not known. Single Population under study; 0 0:H µ µ= t-test. Single t confidence interval. 0x - µt s n = n s t x *± Use when σ is not known. Two populations under study. Two sample t –test. Two sample t confidence interval. 0 1:H 2µ µ= 2 2 2 1 2 1 21 n s n s xx t + − = 2 2 2 1 2 1* 21 nn )xx( sst +±− With n - 1 degrees of freedom (df) Pooled Formulas Estimating σ, by pooling both populations. 2nn s)1n(s)1n(s 21 2 22 2 11 p 2 −+ −+− = Two sample t-test pooled s. Two sample t confidence in 0 1:H 2µ µ= 21 p 21 n 1 n 1s xx t + − = 1 p * 21 nn 1)s()xx( +±− tWith the lesser of n1 -1 or n2 -1 for the degrees of freedom (df). the standard deviations from terval pooled s. 2 1 d.f. = n1 + n2 - 2 C 90% 95% 99% Z* 1.645 1.96 2.576