Probability A event P A of outcomes in A Total of outcomes Rules 1 Or Rule P A or B P A P B only if A B are mutually exclusive P A and B P A P B only if A B are independent 2 General Or Rule P A or B P A P B 3 And Rule 4 General And Rule P A and B P A P B A P B P A B 5 P A B P A only if A B are independent P B A P B only if A B are independent P A B P A and B P B P B A P A and B P A 6 Compliment Rule P Ac 1 P A Random Variables E X X1 P1 X2 P2 X3 P3 E a bx a b Ex E x y E x E y Variance 2 x1 2 P1 x2 2 P2 Var a bx b2 var x Var x y Var x Var y if x and y are independent Standard Deviation square root of var x Binomial Distribution only two possible outcomes success and failure P X Mean np Variance 2 npq SD Square root of npq Normal Distribution 68 falls in 1 SD z score x Variance and Mean Ex are same as above 95 falls in 2 SD 99 7 falls in SD Sampling Distribution One tailed P Value two options greater than or less than Two tailed P Value Not specific Finding P Value On calc stat test 1 prop z test 1 SD pq n 2 Z P assume P someone found something doing it themselves Level of significance If two tailed use 2 Ho P HA 2 tailed HA p 1 tailed HA or P 3 Probability via chart 4 P value value fail to reject P value value reject null hypothesis Confidence Interval 1 Conditions np and nq 10 2 P z pq n 3 If original p is in interval fail to reject Outside interval reject null hypothesis Alpha 2 tailed 1 confidence If the percent is not given 1 tailed 2 2 tailed Errors Type I Null hypothesis is true but we mistakenly reject it Type II Null Hypothesis was false but we failed to reject it Required Sample Size N z 2 p q E2 E margin of error When P isn t given use p 5 Always round up When you decrease ME you increase sample size Z 1 645 1 960 2 326 2 576 99 9 3 29 90 95 98 99 1 05 01 001 1 tailed 1 28 1 645 2 33 3 09 2 tailed 1 645 1 96 2 576 3 29
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