Data Analysis Final Exam

Conditional probability formula

P(B|A) = (P(A and B)) / (P(A)) P(A|B) = (PA and B)) / P(B)

Complement rule

The probability of an event not occurring equals 1 minus the probability that is does occur. P(Ac) = 1 - P(A)

Parameter

value of a population rather than a sample

Point estimate

value we obtain from our one single sample. Single estimate of the parameter

calculating test statistic

z =

Non-disjoint event

it is possible for both (or more) events could be true

Event

list of particular outcomes we are interested in (some subset of the sample)

Margin of error

m = margin of error

Disjoint event

once one event in the sample space occurs, no other event can have taken place

Alternative hypothesis

statement about the same parameter of the population that is exclusive of the null hypothesis (basically the opposite)

Test of a statistical significance

tests a specific hypothesis using data obtained from a sample

Multiplication rule

the probability of some event A occurring AND another event B occurring is the product of their individual probabilities. P(A and B) = P(A) * P(B) **only if the two events are "independent"

Sample space

the set of all possible outcomes of an event

Mean of sampling distribution

unbiased estimate of the population value (the parameter)

Null hypothesis

a specific statement about some parameter of the population (Ho)

Hypothesis test

1. Define Ho and Ha 2. Choose an alpha (e.g. 0.05) 3. Calculate p 4. Compare p and alpha - if p<=alpha reject null hypothesis - if p>alpha fail to reject null hypothesis 5. State conclusion

Hypothesis

an assumption or theory about the characteristics of a variable(s) in a population

SD of sampling distribution

equals the SD of the population divided by the square root of 'n' (standard error)

Sampling variability

If we take multiple random samples, each one is likely to give us a different value

Probability model

Mathematical description of all possible outcomes of a random process (1. sample space 2. probability for every possible outcome in the sample space)

General multiplication rule

P(A and B) = P(A) * P(B|A)

General addition rule

P(A or B) = P(A) + P(B) - P(A and B) **can be used on both disjoint and non-disjoint events

Addition rule for disjoint events

P(A or B) = P(a) + P(B)

Central limit theorem

The theory that, as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution.

Dependent event

if the outcome of one event does affect the probability of the other event

Independent event

if the particular outcome of one event does not affect the probability of the outcomes of the other event