Elementary Statistics Exam #2

Sampling Distribution

Distribution of values taken by the statistic in all possible samples of the same size from the same population.

Discrete

Finite or countable number of values, * typically result from counting. To find probability, we use density curve.

Probability Model

Lists the possible outcomes of a random phenomenon and each outcome's probabilities.

Standardize

z = (x - mu)/sigma

3rd Rule

The complement of any outcome is equal to one minus the outcome. In other words: P(AC)=1−P(A) It is also true then that P(A)=1−P(AC)

2nd Rule

The sum of all of the probabilities for possible events is equal to 1.

5th Rule

Determining the probability that both events occur depends on whether the events are independent or not. This is known as an intersection and is represented by ∩. P(A∩B) is read as "probability of A and B." If two events, A and B, are independent, then the probability of A and B is equal to the product of the two. In other words P(A∩B)=P(A)×P(B). This rule extends beyond two events. For example, if A, B, and C are all independent of one another, then P(A∩B∩C)=P(A)×P(B)×P(C)

Statistics

A number that describes a sample. Statistics are random variables because the value of a statistic varies from sample to sample. variation from sample to sample follows a predictable pattern. Statistics have probability distributions associated with them.

Event

An outcome or set of outcomes of a random phenomenon

Law of Large Numbers

As more observations are added to the sample, the difference between the sample mean and the population mean tends to become smaller.

Binomial Sampling Distribution for Counts

Can be used when the population is at least 20 times as large as the sample. Observations are assumed to be independent, although they are technically dependent.

Factorial Symbol !

Denotes product of decreasing whole numbers. For example 4! = 4∙3∙2∙1=24. We define 0!=1.

4th Rule

Determining the probability that either one or both events occur depends on whether the events are mutually exclusive or not. This is also known as a union and is represented by ∪. P(A∪B) is read as "probability of A or B." Note that this also includes the possibility of both A and B occurring at the same time.

Uniform Distribution

If its values are spread evenly over the range of possibilities. min (1/max)

Continuous

Infinitely many values, * result from measurement.

Probabilities

Must sum up to 1.

Complementary events

One event consists of exactly the outcomes that are not in the other event or the probability of an event not occurring is 1 minus the probability that it does occur. Formula: P(not A) = P(Ac) = 1 − P(A)

Sample Means/Standard Deviation

Sample means are less variable than individual observations. It gets smaller as we take larger samples. The standard deviation decreases in proportion to the square root of the sample size.

Sample Space

Set of all possible outcomes of a random phenomenon

1st Rule

The probability of an impossible event is 0; the probability of a certain event is 1. Therefore, the range of possible probabilities is: 0≤P(A)≤1

Continuous Variable

The probability that X is exactly 0.5 must be 0 (since we have an unknown parameter).

Disjoint events (mutually exclusive)

Two events are disjoint if they have no outcomes in common (or, can never occur simultaneously). Formula: P(A or B) = P(A) + P(B).

Independent events

Two events are independent if knowing that one event occurs does not change the probability that the other occurs. Formula: P(A1 and A2) = P(A1) P(A2) -- depending on how much of the sample there is. If small random samples are taken from large populations without replacement, it is reasonable to assume independence of observations.