PSY201: Chapter 6

Question 1

Introduction to Probability

Answer 1

method for measuring + quantifying likelihood of obtaining specific sample from specific pop
fraction/proportion
probability of specific outcome determined by ratio comparing frequency of occurrence for outcome relative to total # of possible outcomes

Question 2

Introduction to Probability

Answer 2

possible events of interest/# all possible events
Scrabble tiles with the letters A, B, C, & D in a bag, probability of selecting B is:
fraction: p(Btile)=1⁄4
proportion: p(Btile)=1in4 or 0.25

Question 3

Probability of independent event

Answer 3

occurrence of one outcome has no effect on likelihood of occurrence of next event
probability of “tails” is always 0.5, even if, previous flip was a “tails”, previous 2/5 flips were “tails”
Gambler’s fallacy

Question 4

Probability of dependent event

Answer 4

Occurrence of 1 outcome affects probability of another event’s occurrence
sampling without replacement

Question 5

Specific Addition Rule

Answer 5

either/rule for mutually exclusive events
if A or B (or C etc.) will occur
Events must be independent of each other
cannot occur at same time/influence each other
P(A/B) = P(A) + P(B)

Question 6

General Addition Rule

Answer 6

(still either/rule) for events that are not mutually exclusive
events are not mutually exclusive as it is possible for a card to be both a King + a Spade
P(A/B) = P(A) + P(B) – P(A + B)

Question 7

Specific Multiplication rule: Probability of sequence of events

Answer 7

Only valid for independent events: 2 events independent if occurrence of one doesn’t change probability of other occurring
same probability because they are independent

Question 8

Multiplication rule: Probability of sequence of events

Answer 8

Probability of them both occurring is product of probabilities of each occurring
P(A + B) = P(A) x P(B)

Question 9

Conditional Probability: For non- independent events

Answer 9

probability that event B occurs given that event A has occurred
denoted by symbol P(B | A): probability of B given A

Question 10

Conditional Probability: For non- independent events

Answer 10

What is probability of pulling a black card, not replacing it + then pulling a red card from the deck
probability of A x probability of B, given that A has already occurred = p(A) × p(B|A)

Question 11

Probability

Answer 11

necessary to assume random sampling: has 2 requirement

Question 12

Probability

Answer 12

(1) Each indiv in pop has equal chance of being selected

(2) If >1 indiv is selected, probability must stay constant for all selections - random selection with replacement

Question 13

Probability

Answer 13

scores in pop variable ⇒ impossible to predict with perfect accuracy exactly which score or scores will be obtained when you take a sample from the population.
researchers rely on probability to determine relative likelihood for specific samples
possible to determine which outcomes have high probability + which have low probability

Question 14

Probability and the normal distribution

Answer 14

normal distribution useful because many naturally occurring phenomena are distributed in ‘normal’ fashion
pop height/weight/IQ

Question 15

Probability and the normal distribution

Answer 15

Almost all will fall between -3 + +3 SDs from mean
Can compare distributions with each other
Certain % will fall between different points

Question 16

The Theoretical Normal Curve

Answer 16

General relationships:
±1 s = about 68.26%
±2 s = about 95.44%
±3 s = about 99.72%

Question 17

de Moivre and the normal curve

Answer 17

Fled France for England late 17th century
Good friend of Isaac Newton
Expert on chance
Credited for discovering concept of normal curve
first to compute areas under curve as 1, 2, & 3 SDs

Question 18

Carl Gauss

Answer 18

normal curve often called Gaussian distribution, after German mathematician Carl Friedrich Gauss, who discovered many of its properties

Question 19

Properties of the Normal Curve

Answer 19

Theoretical construction
Bell Curve/Gaussian Curve
Perfectly symmetrical normal distribution
mean of a distribution is midpoint of curve

Question 20

Properties of the Normal Curve

Answer 20

tails of the curve are infinite
Mean of curve = median = mode
“area under the curve” is measured in standard deviations from mean

Question 21

Probability and the Normal Distribution

Answer 21

vertical line is drawn through a normal distribution, the following occur:

1. exact location of line can be specified by z-score
2. line divides distribution into two sections: larger section (body) + smaller section (tail)

Question 22

unit normal table

Answer 22

lists several different proportions corresponding to each z-score location
Column A: z-score values
columns B + C: proportions in body + tail, respectively.
Column D: proportion betw mean + z-score location
table values can also be used to determine probabilities

Question 23

Probability and the Normal Distribution

Answer 23

first transform X into z- score ⇒ look up z-score in table + find appropriate proportion/probability

Question 24

Probability and the Normal Distribution

Answer 24

To find X for particular proportion: look up proportion in table + find corresponding z-score ⇒ transform into X

Question 25

Probability and the Binomial Distribution

Answer 25

formed by series of observations for which there are exactly 2 possible outcomes (heads + tails)

Question 26

Probability and the Binomial Distribution

Answer 26

A + B
p(A) = p + p(B) = q
distribution shows probability for each X (# of occurrences of A in series of n)

Question 27

Probability and the Binomial Distribution

Answer 27

When pn + qn are both > 10, binomial distribution closely approximated by normal distribution
mean: μ = pn + SD: σ = √npq
z-score can be computed for each X + unit normal table can be used to determine probabilities for specific outcome

Question 28

Probability and Inferential Statistics

Answer 28

Probability establishes link betw samples + pops

For any known population it is possible to determine probability of obtaining any specific sample

Question 29

Probability and Inferential Statistics

Answer 29

general goal of inferential statistics: use info from sample to reach general conclusion (inference) about unknown pop
Typically researcher begins with sample

Question 30

Probability and Inferential Statistics

Answer 30

sample has high probability of being obtained from specific pop ⇒ researcher can conclude that sample is likely to come from that pop
sample has very low probability of being obtained from specific pop ⇒ reasonable for researcher to conclude specific population is probably not source for sample