Stats

Hypothesis test

A test about a null and alternate hypothesis based on an experiment on a sample of a population to determine whether or not to reject the null hypothesis

H0

Represents the null hypothesis, a statement of the status quo

H1

Represents the alternate hypothesis, a statement that something other than the status quo is occurring

Test statistic

Value commonly calculated from the data used to either find a probability we compare with the significance level or to directly compare with a critical value, to determine whether to reject or accept H0

Critical value/region

Values that the data could take that would result in a rejection of H0

Significance level

The probability chosen by the tester that H0 was true given that you rejected it

Geometric distribution criteria

Successive, independent trials with same probability of success

Assumptions for negative binomial

Successive trials each with constant probability of success

requirements for poisson distribution to be good model

independent

singly in space or time

at a constant average rate in that the mean number in an interval is proportional to the length of an interval

*Critical values

Values on the boundary of the critical region

One tailed test

Single part to the critical region and one critical value

Two tailed test

2 parts to critical region and 2 critical values

Actual significance level

The probability of incorrectly rejecting H0

probability generating function of aX + b

t^b x Gx(t^a)

var(aX+b) when x is a random variable

a²Var(X)

E(aX+b) when x is a random variable

aE(X) + b

E(X+Y) when x and y are random variables

E(X) + E(Y)

requirement for geometric/negative binomial

successive independent trials

constant probability of success

what does central limit theorem state

that given random sample size in normal distribution, sample mean distributed as …..