Behavioral Stats Probability And Random Sampling

Front 1

What is Inferential Statistics?

Back 1

Using data or scores to make a statement about a characteristic of the population. Two statements: hypothesis testing and Parameter estimation.

Front 2

What is hypothesis testing?

Back 2

Experimenter is collecting data in an experiment to validate some hypthesis involving population.

Front 3

What is parameter estimation?

Back 3

Experimenter is interested in determining the magnitude of a population characteristic. Ex. economist interested in what the amount of money a college student spent on food.

Front 4

What is random sampling?

Back 4

sample selected from the population by a process that ensures 1. each possible sample of given size has an equal chance of being selected and 2. all members of population have an equal chance of being selected into sample

Front 5

What is sampling with replacement?

Back 5

Sampling from population one score at a time and then placing it back into the population before drawing again.

Front 6

Sampling without replacement

Back 6

method of sampling in which the members of the sample are not returned to the population before subsequent members are selected.

Front 7

Two ways probability may be approached?

Back 7

1. Priori, or classical viewpoint
2. Posteriori, emperical viewpoint

Front 8

Formula for computing Priori probability?

Back 8

# of A events
p(A)= ----------------------
Total # of events

Front 9

Formula for Posteriori?

Back 9

# times A occurs
p(A) = -------------------------------
Total # of occurrences

Front 10

Properties of Probability

Back 10

1. A proportion ranging from 0.00 to 1.00.
2. Expressed as fraction or decimal #
3. Expressed chances in 100 or p(A) = 0.05 (5 chances in 100)

Front 11

Probability of occurrence of A or B

Back 11

equal to the probability of occurrence of A plus the probability of occurrence of B minus the probability of occurrence of both A and B.

Front 12

Formual for addition rule is

Back 12

p(A or B)=p(A) + p(B) - p(A&B)

Front 13

Two events are mutually exclusive

Back 13

if both CANNOT occur together or if the occurrence of one precludes the occurrence of the other. Ex: Rolling a 1 and a 2 in one roll of a die is mutually exclusive, if it rolls a 1 then it cannot be a 2.

Front 14

Mutually exclusive formula

Back 14

p(A or B) = p(A) + p(B)
always = 0 because the probability of both events occurring together is impossible

Front 15

What is exhaustive?

Back 15

A set of events that includes all of the possible events.
Ex: Rolling a die once, set of events of getting 1, 2, 3, 4, 5, 6, is exhaustive because set includes all possible events.

Front 16

Multiplication rule

Back 16

concerned with joint or successive occurrence of several events

Front 17

Probability of occurrence of both A and B

Back 17

equal to the probability of occurrence of A times the probability of occurrence of B given A has occurred

Front 18

Multiplication rule equation

Back 18

p(A and B) = p(A) p(B/A)

p(B/A) means "probability of occurrence of B given A has occurred.)

Front 19

Multiplication rule: Mutually exclusive events

Back 19

p(A and B) = 0

Front 20

Two events are Independent

Back 20

if the occurrence of one has no effect on the probability of occurrence of the other

Front 21

Ex of two events being independent

Back 21

Suppose we draw two cards, one at a time, with replacement, from ordinary deck of cards. Let A be first card drawn and B be second card. Since A is replaced before drawing B the occurrence of A on first draw has no effect on probability of occurrence of B

Front 22

Equation for multiplication rule with independent events

Back 22

p (A and B) =p (A) p (B/A) = P(A)p(B)

Front 23

Multiplication with dependent events

Back 23

When A and B are dependent the probability of occurrence of B is affected by the occurrence of A

Front 24

Equation for multiplication rule with dependent events

Back 24

p(A and B) = p(A) p (B/A)

Front 25

Ex of dependent events

Back 25

Suppose we draw two cards one at a time, without replacement. A is an ace on first draw and B is an ace on the second draw.
p(an ace on the first draw and an ace on the second draw) = p(an ace on the first draw) p(an ace on the second draw, given an ace was obatained on first draw)

Front 26

Multiplication and addition rules

Back 26

p(A) = p(5 die 1 & 6 die 2)
= p(5 die 1) p(6 die 2)
= (1/6) (1/6) = 1/36
p(B) = p(6 die 1 and 5 die 2)
= p(6 die 1) p(5 die 2)
= (1/6) (1/6) = 1/36
p(+ of 11)=p(A or B)=p(A)+p(B)

Front 27

Probability and Normally distributed continuous variables

Back 27

Area under curve corres A
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Total area under curve