Module 8

Question 1

 product of hypothesis testing via various statistical tests and is claimed to be significant (i.e. not due to chance) most commonly when the value is 0.05 or less
 It cannot provide information about what size of an effect is or what the effect size is likely to be on the total population
 Value 0.05 is arbitrary; simply a convention amongst statistician that this value is deemed the cutoff level for significance

Answer 1

P-value

Question 2

 can be anything from 0.80 (80%) to 0.99 (99%) depending on requirements to avoid too many subjects being recruited for a study
 Drawback in the calculations do not take variation of data into account

Answer 2

Power

Question 3

 aka “False Positive”
 Error of rejecting the null hypothesis when it is actually true
 Error of accepting an alternative hypothesis (real hypothesis of interest) when the results can be attributed to chance
 Occurs when we are observing a difference when in truth there is none (or there is no statistically significant difference)

Answer 3

TYPE I ERROR

Question 4

 aka “False Negative”
 Error of NOT rejecting the null hypothesis when the alternative hypothesis is the true state of nature
 Error of failing to accept an alternative
hypothesis when you don’t have adequate power
 Occurs when we are failing to observe a difference when in truth there is one

Answer 4

TYPE II ERROR

Question 5

 measure of the researchers’ uncertainty in the sample statistic as an estimate of the population parameter, if less than the whole population is studied usually set at 95% by convention

Answer 5

CONFIDENCE INTERVAL

Question 6

 Shrink with increasing sample size, the researcher should be seeking to reach an optimal size, rather than the maximal sample size

Answer 6

STANDARD ERROR

Question 7

 i.e. standard deviation, effect of being studied e the less variability in the sample, the more precise the estimate in the population and therefore a narrower range

Answer 7

THE MEAN AND THE VARIABILITY

Question 8

 The more confident someone wants to be in the obtained results, the higher the confidence interval needs to be.
 Conversely, in a 90% confidence interval is considered sufficient then the range of data required will be narrower, and hence the required sample size will be smaller

Answer 8

DEGREE OF CONFIDENCE

Question 9

any process of generating a set of data or observations that can be repeated under basically the same conditions, which lead to well-defined outcomes.

Answer 9

Random experiment

Question 10

set all possible outcomes of an experiment
o usually denoted by S

Answer 10

Sample space

Question 11

element of the sample space; an outcome

Answer 11

Sample point

Question 12

any subset of the sample space

Answer 12

Event

Question 13

a subset of the sample space that contains no elements
o Denoted by the symbol f

Answer 13

Null space (Empty Space)

Question 14

– event which contains only
one element of the sample space

Answer 14

Simple event

Question 15

event that can be expressed as the union of simple events; contains more than one sample point

Answer 15

Compound event

Question 16

two events A and B are mutually exclusive which means that A and B have no elements in common

Answer 16

Mutually exclusive events

Question 17

empty space can be viewed as an event that will never happen

Answer 17

Impossible event

Question 18

the sample space S, as an event always occurs
o Also referred to as certain

Answer 18

Sure event

Question 19

shows intersection of events A and B
o Event that both A and B occur

Answer 19

A ∩ B

Question 20

– shows union of events A and B
o Event that A or B or both occur

Answer 20

A ∪ B

Question 21

shows complement of an event A with respect to S
o Contains all elements of S that are
not in A and is the event that A does
not occur

Answer 21

A^1 or A^c

Question 22

 Determined even before the experiment is performed using the following rule:
 If an experiment can result in any N different equally likely outcomes, and if exactly n of these outcomes corresponds to event A, then the probability of event A is

Answer 22

Priori (Classical Probability)

Question 23

 Determined by repeating the
experiment a large number of times

Answer 23

Posteriori (Relative Frequency/ Empirical Probability)

Question 24

 Probability is determined by the use of intuition, personal beliefs, and other indirect information

Answer 24

Subjective Probability

Question 25

An arrangement or ordering of all or part of a set of objects.

Answer 25

Permutation

Question 26

selection of r objects from n without regard to order

Answer 26

Combination

Question 27

 The probability of an event B occurring
when it is known that some event A has
occurred
It is defined by the equation
P(B | A) = “P(A∩B)” /”P(A)” if P (A) > 0

Answer 27

Conditional Probability

Question 28

P (B | A) is read as

Answer 28

“probability of B given A”

Question 29

 Function whose value is a real number determined by each element in the sample space

Answer 29

Concept of Random Variable

Question 30

 If a sample space contains a finite number of possibilities or an unending sequence with as many elements as there are whole numbers

Answer 30

Discrete sample space

Question 31

 Random variable defined over a discrete
sample space

Answer 31

Discrete random variable

Question 32

 Table or formula listing all possible values that a discrete random variable can take on, along with the associated probabilities
 The probabilities associated with all possible values of a discrete random variable must sum to 1

Answer 32

Discrete Probability Distribution

Question 33

sample space contains an infinite number of possibilities equal to the number of points on a line segment

Answer 33

Continuous sample space

Question 34

 Random variable defined over a continuous sample space

Answer 34

Continuous random variable