Exam II Review

Question 1

Classical approach

Answer 1

P(E) = Possible outcomes where E occurs / Total possible outcomes

Question 2

Relative frequency approach

Answer 2

P(E) = Trials where E occurs / Total trials

Question 3

Subjective approach

Answer 3

P(E) = Best guess

*Use when trials aren’t possible

Question 4

Sample space

Answer 4

A collection or a set of possible outcomes of a random experiment

Question 5

Unions

Answer 5

At least one of a number of possible events occurs.

A or B

Question 6

Conjunctions

Answer 6

Two or more events all occur.

A and B

Question 7

Marginal probability

Answer 7

The probability that a “simple” event will occur

Question 8

Joint probability

Answer 8

The probability that two or more
events occur together

Question 9

Conditional probability

Answer 9

The probability that an event occurs,
given that another event occurs

Question 10

Independent events

Answer 10

The occurrence of A does not predict the occurrence of B. (And vise versa)

Question 11

Testing for independence

Answer 11

Events A and B are independent if and only if
 P(A|B) = P(A)
 P(B|A) = P(B)
 P(A and B) = P(A) x P(B)
If any one of these statements is true, the others are also true, and if any one of these statements is false, the others are also false.

Question 12

Dependent events

Answer 12

The occurrence of one does help predict the occurrence of another

Question 13

Inverse conditional probabilities

Answer 13

Generally, conditional probabilities cannot be inversed.

(As with most things, there are exceptions)

Question 14

Discrete probability distribution

Answer 14

A list of all possible values of a discrete random variable X, with their respective probabilities

 The list of outcomes is exhaustive.
 The outcomes are mutually exclusive.
 The probabilities sum to 1.

Question 15

Continuous probability distribution

Answer 15

Have probability density functions (PDFs)

Question 16

Parameter

Answer 16

Numerical descriptors of a population
 Values usually unknown

Question 17

Statistic

Answer 17

Numerical descriptors of a sample
 Calculated from observations in the sample

Question 18

Sampling error

Answer 18

Different samples will yield different values for the same statistic.
 Different samples have different sample
means and standard deviations.

Question 19

Sampling distributions

Answer 19

Probability distributions of multiple samples drawn from the same population that represent one sample statistic (such as mean or standard deviation)

Question 20

Standard error

Answer 20

The standard error is a standard deviation, but the special name emphasizes that it’s the standard deviation of the sampling distribution.

Question 21

Central Limit Theorem

Answer 21

As n increases, the distribution of
x-bar becomes normal and gets skinnier

Question 22

Point estimates

Answer 22

A point estimate is a single number.
 x-bar is a point estimate for μ.
 A point estimate is unbiased if on average it
equals the thing we’re trying to estimate.

Question 23

Interval estimates

Answer 23

An interval estimate for the population mean is a range of possible
values for μ.

Question 24

Factors that affect CI width

Answer 24

Confidence level, sample size, and standard deviation of the population

Question 25

Null hypothesis

Answer 25

An assertion that nothing is going on

Question 26

Alternative hypothesis

Answer 26

Compliment of the null, usually is the claim we want to make

Question 27

Significance level

Answer 27

Alpha level, used to conclude if we can reject the null hypothesis, chosen threshold for saying that the probability of xbar is small enough to reject the null hypothesis, usually .05.

Question 28

Critical values

Answer 28

Correspond to the significance level

Question 29

P-value

Answer 29

Probability associated with the observed result

Question 30

Rejection-region approach

Answer 30

Does the test statistic exceed the critical value?

Question 31

P-value approach

Answer 31

Is the p value less than the significance level?

Question 32

Lowering the significance value _______ the critical values.

Answer 32

increases

Question 33

Type I error

Answer 33

Rejecting the null when you shouldn’t

Question 34

Type II error

Answer 34

Failing to reject the null when you should

Question 35

Power

Answer 35

Probability of rejecting the null hypothesis, assuming that a specific alternative hypothesis is true

Question 36

What affects power?

Answer 36

1. Is it a one or two-tailed test (two-tailed yields lower power)
2. As the difference between mu and mu0 increases, power increases
3. As the sample size increases, the power for rejecting the null hypothesis increases.

Question 37

t distribution

Answer 37

Used when population sd is unknown, not a normal curve like the z distribution

Looks like a standard normal distribution, but it is wider (it has thicker tails).

Question 38

Degrees of freedom

Answer 38

The degrees of freedom are equal to the number of values that are “free to vary” once some information about them is already known.

For t tests, df = n-1

Question 39

Effect size

Answer 39

A value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity