Binomial Distribution

Question 1

Binomial distribution

Answer 1

a probability distribution that results when:
- there is a series of N trials
- on each trial, there are only two possible, mutually exclusive, outcomes
- there is independence between the outcomes of each trial
- the probability of each possible outcome on any trial stays the same from trial to trial

Question 2

Binomial table

Answer 2

shows all possible outcomes and associated probabilities for any binomial distribution up to N=20

if P is higher number than represented on table, reverse it (ie, if P=.75, look at .25)

Question 3

What are the two hypotheses that can be formulated for any observation?

Answer 3

the null hypothesis
the alternate hypothesis

mutually exclusive and exhaustive

Question 4

Null hypothesis

Answer 4

H0 (0 is subscript)
the observation is due to chance or random factors
- more conservative, baseline assumption

Question 5

Alternate hypothesis

Answer 5

H1 (1 is subscript)
the observation is not due to chance or random factors

• evidence to support H1 often suggests something new has been discovered or demonstrated
• if you do not accept H1, you “retain” or “fail to reject” H0
  (we cannot conclude… or, this experiment does not provide evidence that…)

Question 6

Alpha level (α)

Answer 6

an evidentiary standard set by the researcher before the study; defines how strongly the sample evidence must contradict the null hypothesis before you can reject it for the entire population

affects the probability of Type I and Type II errors
- more strict –> reduce chance of Type I (false alarm), but increase chance of Type II (miss)

Question 7

decision rule

Answer 7

clear cutoff given by α (alpha level) for whether to reject or retain H0 (null hypothesis)
- if the obtained probability ≤ α, REJECT H0
- if the obtained probability > α, RETAIN H0

Question 8

Normal approximation approach

Answer 8

with large numbers, normal distribution can be used to approximate binomial probabilities

Question 9

Type I error

Answer 9

a decision to reject H0 when in fact H0 is true
- false alarm

Question 10

Type II error

Answer 10

a decision to retain H0 when in fact H0 is false
- a “miss”

Question 10

Type II error

Answer 10

a decision to retain H0 when in fact H0 is false
- a “miss”

Question 11

Directional hypothesis

Answer 11

one-tailed hypothesis that states the direction of the difference or relationship

• only use if you have strong justification for formulating directional alternate hypothesis

Question 12

Non-directional hypothesis

Answer 12

two-tailed hypothesis predicts that the IV will have an effect on the DV, but the direction of the effect is not specified

• more conservative approach