Population standard deviation known Population standard deviation unknown Sample standard deviation M x z n x margin of error Sample Size n z 2 2 e2 Hypothesis Testing 1 Sample x value sample standard deviation n sample size z z score M x t s n x value s population standard deviation n sample size t t score n sample size standard deviation e desired margin of error Interval estimate of a population proportion P p p 1 p n p sample proportion n sample size z z score Pop std deviation known Sample std deviation known Pop Proportion z x n mean standard deviation n sample size z z score t x s n DF n 1 Point estimate p x n z p p p 1 p n p sample proportion x of elements in sample n sample size p mean population proportion H 0 3 2 1 Sample std deviation known Pop Proportion t x 1 x 2 s1 1 s2 2 n1 n2 DF n1 n2 2 Point estimate p1 x n Point estimate p2 x n Hypothesis Testing 2 Sample Pop std deviation known z x 1 x 2 1 1 2 2 n1 n2 Z values 05 01 1 tail 1 65 Point estimator of P when p1 p2 p3 2 33 p n1p1 n2p2 n1 n2 2 tail 1 96 2 58 Test Stat z p1 p2 p 1 p 1 n1 1 n2 y b0 b1x 1 r 1 0 r2 1 R2 SSR SST explained variation total variation Test stat Fcalc MSR MSE Fcrit F chart DF1 H across 1 0 0 DF2 down H 1 0 a Standard Error p 1 p 1 n1 1 n2 Complement of A P A 1 P A Addition law Independent events P A B P A or P B A P B P A B P A P B P A B Mutually exclusive events Multiplication law P A B P B P A B P A B P A P B A P A B 0 Multiplication law for independent events