Hypothesis Testing Cheat Sheet

Hypothesis Testing Cheat Sheet Type Population Mean Condition Difference between Population Variances puremathematics.mt Notes H 0 : μ=μ0 H 1 : μ ≠ μ 0 / μ >μ 0 / μ <μ 0 X̄ −μ Z= σ √n Z follows the the standard normal distribution. σ is known n is small ( n≤30 ) H 0 : μ=μ0 H 1 : μ ≠ μ 0 / μ >μ 0 / μ <μ 0 X̄− μ t= σ √n t follows the t distribution with n−1 d.o.f. σ is unknown n is large ( n>30 ) H 0 : μ=μ0 H 1 : μ ≠ μ 0 / μ >μ 0 / μ <μ 0 Z= σ is unknown n is small ( n≤30 ) H 0 : μ=μ0 H 1 : μ ≠ μ 0 / μ >μ 0 / μ <μ 0 t= H 0 : π =π 0 H 1 : π ≠ π 0 / π >π 0 / π <π 0 Z= H 0 : π 1−π 2=0 H 1 : π 1−π 2 ≠ 0 / π 1−π 2> 0 / π 1−π 2< 0 Z= Difference between Population Proportions Population Variance Statistic 99271274 σ is known n is large ( n>30 ) Population Proportion Difference between Population Means Hypothesis debonomark@gmail.com σ 1 , σ 2 are known X̄ −μ s √n Z follows the the standard normal distribution. X̄− μ s √n t follows the t distribution with n−1 d.o.f. H 0 : μ1 −μ 2=μ0 H 1 : μ1−μ 2 ≠ μ 0 / μ1−μ2 > μ0 / μ1−μ2 < μ0 Z= σ 1 , σ 2 are unknown σ 1 , σ 2 are unequal n1 , n2 are large H 0 : μ1 −μ 2=μ0 H 1 : μ1−μ 2 ≠ μ 0 / μ1−μ2 > μ0 / μ1−μ2 < μ0 Z= σ 1 , σ 2 are unknown σ 1 , σ 2 are equal H 0 : μ1 −μ 2=μ0 H 1 : μ1−μ 2 ≠ μ 0 / μ1−μ2 > μ0 / μ1−μ2 < μ0 t= 2 2 H 0 : σ =σ 0 H 1 : σ 2 ≠ σ 20 2 Z follows the the standard normal distribution. π (1−π ) n p1− p2−(π 1−π 2) P(1−P)( 1 1 + ) n1 n2 x¯1− x¯2−( μ 1−μ 2) √ √ 2 χ 2= 2 F= 2 s2 Z follows the the standard normal distribution. 2 Z follows the the standard normal distribution. 2 s1 s 2 + n1 n2 S 2p ( 1 1 + ) n1 n2 (n−1)s σ2 s1 subjects in group 1, 2 resp. that have the characteristic 2 x¯1− x¯2−( μ 1−μ 2) √ Z follows the the standard normal distribution. x +x P= 1 2 where x 1 , x 2 is the number of n1 +n 2 σ1 σ 2 + n1 n2 x¯1− x¯2−(μ 1−μ2) 2 H 0 : σ 1= σ 2 2 2 H 1: σ 1≠σ 2 √ √ p−π 2 t follows the t distribution with n1 +n2−2 d.o.f. χ 2 follows the χ 2 distribution with n−1 d.o.f. F follows the F distribution with n1−1 and n2−1 d.o.f.