ISDS 2000 Exam 2 Review

To calculate the probability of the union of two mutually exclusive events A and B

we add the probability of A to the probability of B

Unconditional probabilities are also known as _________ probabilities.

Marginal

Stratified Sample includes

- randomly selected observations from each stratum - the number of observations per stratum is proportional to the stratum's size in the population - the data for each stratum are eventually pooled

Standard Transformation

A normally distributed random variable X with mean μ and standard deviation σ can be transformed into the standard normal random variable Z as Z = (X -μ)/σ.

Proabability

A numerical value that measures the likelihood that an event occurs; this value is between 0 & 1

Simple Random Sample

A sample of n observations has the same probability of being selected from the population as any other sample of n observations

Standard Normal Distribution

A special case of the normal distribution with a mean equal to zero and a standard deviation (or variance) equal to one

Complement Rule

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

Standard Normal Table (z table)

Provides cumulative probabilities P(Z ≤ z) for positive and negative z values.

Selection Bias

Refers to a system underrepresentation of certain groups form consideration for sample

Intersection (A ∩ B)

The event consisting of all outcomes A and B

Normal Probability Distribution

The most extensively used probability distribution in statistical work and the cornerstone of statistical inference.

Cluster Sampling

The population is first divided into mutually exclusive and collectively exhaustive groups called clusters

Point Estimator

a function of the random sample used to make inferences about the value of an unknown population parameter

Parameter

constant; its value may be unknown

Mutually Exclusive Events

contain all outcomes; do not share any common outcome of an experiment

Expected Value of the Sample Proportion

equal to the population proportion; E(P) = p

Expected Value of the Sample Mean

equals the population mean or E(X̅) = μ; the sample mean is an unbiased estimator of the population mean

The normal distribution approximating is justified when

n ≥ 30

Empirical and classical probabilities are often grouped as ____________ __________.

objective probability

Cluster Sample includes

observations from randomly selected clusters

We use R's _______ function to find probabilities associated with the normal distribution.

pnorm

We use sample statistics to make inferences about the unknown ___________ _________.

population parameter

Standard Deviation of the Sample Mean

referred to as the standard error of the sample mean; se(X̅) = σ/√n

Standard Deviation of the Sample proportion

referred to as the standard error of the sample proportion; se(P) =√ p (1-p) / n

Most statistical methods presume

simple random samples

What makes a "good" sample?

It is representative of the population we are trying to describe

For mutually exclusive events A and B, the joint probability is _______

Zero

In order to convert a contingency table into a joint probability table, the frequency of each cell is divided by the

total number of outcomes in the sample space

If X̅ is normally distributed, then any value x̄ can be transformed into its corresponding z given by

z = x̄ - μ / σ/√ (n)

Sample Space (S)

All possible outcomes of an experiment

Exhaustive Events

All possible outcomes of an experiment belong to the events

Stratified vs. Cluster Sampling

- In stratified sampling, the sample consists of observations from each group, whereas in cluster sampling, the sample consists of observations from the selected groups. - Stratified sampling is preferred when the objective is to increase precision, and cluster sampling is preferred when the objective is to reduce costs.

Normal Distribution traits

- bell-shaped - symmetric - mean, median, and mode are all equal - described by two parameters (the population mean, μ, and the population variance σ^2) - asymptotic: the tails get closer and closer to the horizontal axis but never touch it.

Estimate

A particular value of an estimator

Subjective Probability

A probability value based on personal and subjective judgement.

Experiment

A process that leads to one of several possible outcomes

Inverse Transformation

A standard normal variable Z can be transformed to the normally distributed random variable X with mean and standard deviation as X = μ + Zσ

Event

A subset of a sample space.

Sample

A subset of the population

Simple Event

An event consisting of only one outcome

Empirical Probability

Calculated as a relative frequency of occurrence

__________ probabilities are based on the assumption that all outcomes of an experiment are equally likely

Classical

Population

Consists of all items of interest in a statistical problem

Complement

For any given event, the probability of that event and the probability of the ____________ of the event must sum to one.

Addition Rule

P(A U B) = P(A) + P(B) - P(A ∩B)

Joint Probability

P(A ∩ B)

Multiplication Rule

P(A ∩ B) = P(A|B) * P(B)

Social-Desirability Bias

Refers to a systematic difference between a group's "socially acceptable" responses to a survey or poll and this group's ultimate choice

Nonresponse Bias

Refers to a systematic difference in preferences between respondents and non respondents to a survey or a poll

Bias

Refers to the tendency of a sample statistic to systemically overestimate a population parameter

Low of Large Numbers

The empirical probability approaches the classical probability if the experiment is run a very large number of times

Union (A U B)

The event consisting of all outcomes A or B

Complement A(A^c),

The event consisting of all outcomes in the sample space that are not in A

Dependent Events

The outcome of one event does affect the outcome of the second event

Stratified Random Sampling

The population is first divided up into mutually exclusive and collectively exhaustive groups called strata

Conditional Probability

The probability of an event given that another event has already occurred; P(A|B) = P(A ∩ B) / P(B)

Unconditional Probability

The probability of an event without any restriction

Impossible Event

The probability of the event is 0

Definite Event

The probability of the event is 1

Central Limit Theorem (CLT)

The sum or mean of a large number of independent observations from the same underlying distribution has an approximate normal distribution

Joint

The values in the interior of a contingency table represent __________ probabilities

Joint Probability

The values in the interior of a joint probability table, representing the probabilities of the intersection of two events

Marginal Probability

The values in the margins of a joint probability table that represent unconditional probabilities

Independent Events

Two or more events in which the outcome of one event does not affect the outcome of the other event(s); P(A ∩ B) = P(A) x P(B)

Statistic

a random variable whose value depends on the chosen random sample

Estimator

a statistic used to estimate a population parameter

Classical Probability

based on logical analysis rather than on observation or personal judgement