I Probability Chapter 4 Joint Probability Conditional probability P A B P A B P B Probability A numerical measure of the likelihood that an event will occur Complement of A The event consisting of all sample points that are not in A P A 1 P A Union of A and B The event containing all sample points belonging to A or B or both The union is denoted A B OR Intersection of A and B The event containing the sample points belonging to both A and B The intersection is denoted A B AND Addition law A probability law used to compute the probability of the union of two events OR P A B P A P B P A B Mutually exclusive events Events that have no sample points in common that is A B is empty P A B 0 Conditional probability The probability of an event given that another event already occurred Given prior info The conditional probability of A given B P A B P A B The conditional probability of B given A P B A P A B P B P A Joint probability The probability of two events both occurring that is the probability of the intersection of two events Marginal probability The values in the margins of a joint probability table that provide the probabilities of each event separately Independent events Two events A and B where P A B P A or P B A P B that is the events have no influence on each other Multiplication law A probability law used to compute the probability of the intersection of two events P A B P B P A B P A B P A P B A Multiplication law for independent events P A B P A P B II Discrete distributions Chapter 5 Binomial p x p n n px 1 p n x x of success p probability of successes on trial n of trials x n x 2 possible outcomes for each trial success failure 1 Sequence of n identical trials 2 3 The probability of success p does not change from trial to trial 4 The probability of failure 1 p does not change from trial to trial 5 Trials are independent not affected by others Poisson p x e x x expected value or mean of occurrence f x probability of x success in n trials 1 Probability of occurrence is same for any 2 intervals of equal length 2 Occurrence nonoccurrence in any interval is independent of the occurrence in any other interval Given probability of successes sample size Given average per unit basis no sample size III Confidence Intervals Chapters 7 8 Mean z x n mean standard deviation n sample size z z score Proportion z p p p 1 p n p sample proportion x of elements in sample n sample size p mean population proportion Point estimate p x n Population standard deviation known Population standard deviation unknown Sample standard deviation M x z n x margin of error 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 1 Compute upper tail area 2 Compute degrees of freedom N 1 95 2 4750 5 Chart z 1 96 Upper tail area Sample Size n z 2 2 e2 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 IV Hypothesis Testing 1 Sample Chapter 9 1 Hypothesis Ho 20 Null H 20 Alternative Put conditions to prove here ex less than 20 2 Graph 1 tail if greater than equal to less than equal to 2 tail both sides find Zcrit or Tcrit with tables 3 Decision rule 4 Calculate test stat If test stat z is 1 96 or 1 96 reject Ho Otherwise do not reject 5 Conclusion Reject Ho Do not reject Ho 6 Evidence supports the claim that Evidence does not support the claim Pop std deviation known Sample std deviation known Pop Proportion Pop std deviation known Sample std deviation known Pop Proportion z x n t x s n V Hypothesis Testing 2 Sample Chapter 10 z x 1 x 2 1 1 2 2 n1 n2 Point estimator of P when p1 p2 p3 p n1p1 n2p2 n1 n2 t x 1 x 2 s1 1 s2 2 n1 n2 DF n1 n2 2 z p p p 1 p n Point estimate p x n Point estimate p1 x n Point estimate p2 x n Test Stat z p1 p2 p 1 p 1 n1 1 n2 1 tail 2 tail Z values 05 01 1 65 2 33 1 96 2 58 VI Simple linear regression Chapter 14 POSSIBLE REGRESSION LINES IN SIMPLE LINEAR REGRESSION Standard Error p 1 p 1 n1 1 n2 1 Diagram scatter diagram 2 Identify model Specify values of coefficients y b0 b1x yDV b0 b1xIV 3 Test predict outcomes Plug in a random for X to get Y value Plug in a value included in the data for X to get Y value 4 How well does model predict changes in dependent variables 1 r 1 0 r2 1 Regression R2 SSR SST explained variation total variation R2 represents that IV is responsible for variation 5 Is the model significant H0 1 0 Ha 1 0 Find Fcrit F chart DF1 across DF2 down Calculate Test statistic F MSR MSE Reject H0 if F F The coefficient for the variable is not 0 and therefore belongs in the model