Statistics 2
Probabilities
08-01-2023
1
,Table of Contents
Parameters........................................................................................................................3
Basic Formulas...................................................................................................................4
Multiplication Rule.............................................................................................................4
Addition Rule.....................................................................................................................5
Complement Rule...............................................................................................................5
Conditional Probability.......................................................................................................5
Probability Keywords.........................................................................................................6
What to use when?............................................................................................................7
Dependent & Independent...............................................................................................10
Probability Distribution....................................................................................................10
Binominal Distribution.....................................................................................................11
Normal Distribution.........................................................................................................12
Sampling Errors................................................................................................................13
Sampling Distribution.......................................................................................................13
Confidence Interval..........................................................................................................14
Central Limit Theorem................................................................................................................16
Hypothesis Testing...........................................................................................................18
Two-tailed hypothesis testing...........................................................................................19
T-test................................................................................................................................21
T-test with two samples...................................................................................................22
Chi-square Analysis (Contingency Analysis)......................................................................24
2
, Parameters
Symbol Meaning Extra info
P-value Probability P = always between 0 and 1
(%)
n Number of trials
n Sample size
X Random variable (how many
of a certain outcome)
Ex Expected value What you expect to find
most often. (or on average)
µ Population mean (Mu)
x Sample mean
σ Standard deviation (Sigma)
σx Standard error
μx Mean sampling distribution
H0 Null hypothesis (status Innocent
quo/claim)
HA Alternative hypothesis Guilty
(Researcher’s hypothesis)
3
Probabilities
08-01-2023
1
,Table of Contents
Parameters........................................................................................................................3
Basic Formulas...................................................................................................................4
Multiplication Rule.............................................................................................................4
Addition Rule.....................................................................................................................5
Complement Rule...............................................................................................................5
Conditional Probability.......................................................................................................5
Probability Keywords.........................................................................................................6
What to use when?............................................................................................................7
Dependent & Independent...............................................................................................10
Probability Distribution....................................................................................................10
Binominal Distribution.....................................................................................................11
Normal Distribution.........................................................................................................12
Sampling Errors................................................................................................................13
Sampling Distribution.......................................................................................................13
Confidence Interval..........................................................................................................14
Central Limit Theorem................................................................................................................16
Hypothesis Testing...........................................................................................................18
Two-tailed hypothesis testing...........................................................................................19
T-test................................................................................................................................21
T-test with two samples...................................................................................................22
Chi-square Analysis (Contingency Analysis)......................................................................24
2
, Parameters
Symbol Meaning Extra info
P-value Probability P = always between 0 and 1
(%)
n Number of trials
n Sample size
X Random variable (how many
of a certain outcome)
Ex Expected value What you expect to find
most often. (or on average)
µ Population mean (Mu)
x Sample mean
σ Standard deviation (Sigma)
σx Standard error
μx Mean sampling distribution
H0 Null hypothesis (status Innocent
quo/claim)
HA Alternative hypothesis Guilty
(Researcher’s hypothesis)
3
