Stat Studying

Question 1

Retrospective vs. Prospective Study

Answer 1

Retrospective looks backward at past data; prospective follows subjects forward into the future.

Question 2

Case-Control Study

Answer 2

A study comparing people with a condition (“cases”) to people without it (“controls”) to find possible causes.

Question 3

Rule for Concluding Cause and Effect

Answer 3

Only when the study is a randomized controlled experiment, not an observational study.

Question 4

Interacting/Confounding Variable

Answer 4

A variable linked to both the explanatory and response variable that can distort the apparent relationship.

Question 5

Hawthorne Effect (Experimenter Effect)

Answer 5

When participants change behavior because they know they’re being observed.

Question 6

Random Circumstance

Answer 6

A situation with uncertain outcomes, even if repeated under identical conditions.

Question 7

Probability of an Event

Answer 7

The long-run proportion of times an outcome occurs in repeated trials.

Question 8

Personal vs. Relative Frequency Probability

Answer 8

Personal = subjective belief; Relative frequency = based on data from repeated trials.

Question 9

Sample Space

Answer 9

The set of all possible outcomes in a random circumstance.

Question 10

Simple vs. Compound Event

Answer 10

Simple = one outcome; Compound = multiple outcomes combined.

Question 11

Complement of an Event

Answer 11

P(A^c) = 1 - P(A)

Question 12

Mutually exclusive events

Answer 12

Events that cannot occur together (no overlap).

Question 13

Conditional probability

Answer 13

The probability that one event occurs given another event already occurred; P(A∣B)

Question 14

Independent events

Answer 14

When knowing one occurs doesn’t affect the probability of the other; P(A∣B)=P(A)

Question 15

Sampling With vs. Without Replacement

Answer 15

With replacement = items returned, probabilities stay same; Without = not returned, probabilities change.

Question 16

Bayes’ Theorem

Answer 16

It updates probabilities using new information; P(A∣B)=
P(A)P(B∣A)/P(B)

Question 17

Gambler’s Fallacy

Answer 17

The mistaken belief that past random outcomes affect future ones.

Question 18

Random Variable

Answer 18

A numerical value assigned to outcomes of a random circumstance.

Question 19

Discrete v. Continuous Random Variable

Answer 19

Discrete = countable outcomes; Continuous = measured on a continuum.

Question 20

Probability Distribution (PDF)

Answer 20

A rule or table that gives the probability for each possible value of a random variable.

Question 21

Cumulative Probability Function

Answer 21

Add up values of all probabilities before and equal

Question 22

Binomial Random Var

Answer 22

Number of successes in n independent trials with same probability p

Question 23

Binomial Experiment

Answer 23

Fixed n, two outcomes, independent trials, constant probability of success.

Question 24

Expected Value (Discrete RV)

Answer 24

Multiply each outcome by its probability and sum:
E(X)=∑xP(x).

Question 25

Variance and Standard Deviation (Discrete RV)

Answer 25

Var(X) is the sum of difference in values and mean squared times probability and then standard deviation is square root of that ​

Question 26

Probability Density Function (Continuous RV)

Answer 26

A curve where area under it = probability; total area = 1.

Question 27

Uniform Random Variable

Answer 27

All outcomes equally likely; pdf is flat.

Question 28

Normal Random Variable

Answer 28

Follows a bell-shaped, symmetric distribution defined by mean (μ) and SD (σ).

Question 29

Standard Normal Curve

Answer 29

Normal distribution with μ=0,σ=1; uses z-scores.

Question 30

Z-score

Answer 30

The number of standard deviations a value is from the mean: z=x−μ/σ