statistics S2

Definition (S2)

Justify skewness of a distribution
-mean < median < mode
-negative skewed

For Poisson model
-used when mean = variance
as Y~N(N,N)

Conditions for Poisson distribution:-
-events occur independently/randomly
-events occur singly
-events occur at a constant rate

Conditions for Binomial distribution:-
-fixed number of trial
-independent trials
-only have two possible outcomes
-probability of success is constant

Conditions for Binomial => Poisson = Poi(np)
-n is large, n>50
-p is small, p<0.2

Conditions for Binomial => Normal = N[np, np(1-p)]
-n is large
-p close to 0.5

Condition for Poisson => Normal = N(m,m)
-mean,m>10 or large

Statistic
-a random variable calculated as
-a function of known observation from a population
@-a random variable that is a function of a random sample that contain no other unknown parameter

Population
-a complete collection of items or individual

Census
-is when every member if the population is investigated
-adv: total accuracy
-disadv: time consuming to obtain data and analyse it / expensive / hard to analyse data, difficult to carry out / destructive testing

Sample
-a selection of individual members of population
-adv: saves time / cheaper / easier / used when testing results in destruction of item
-disadv: uncertaincy due to natural variation / uncertaincy due to bias / possible bias as sampling frame incomplete / bias due to subjective choice of sample / bias due to non-response

Sampling Frame
-a list of all sampling units or all the population

Sampling Unit
-individual member of the population or sampling frame

Sampling Distribution
-all possible sample are chosen from a population
-the values of a statistic and the associated probability is a sampling distribution
@-the distribution of all possible sample ... for all sample of size ...

Hypothesis Test
-is a mathematical procedure to examine a value of a population parameter proposed by the null hypothesis compared with an alternative hypothesis.

Null Hypothesis, Ho
-is a claim / assumption that is assumed to be true until it is proven otherwise.

Alternative Hypothesis, H1
-is an alternative claim / assumption that against the null hypothesis, if the null hypothesis is proven false, then the alternative hypothesis will be accepted.

Critical Region
-is the range of values that would lead to rejection of null hypothesis
@-a range of values of a test statistic such that if a value of the test statistic obtained from a particular sample lies on the critical region, than the null hypothesis is rejected

Critical Value(s)
-boundary value(s) of the critical region

Significance Level
-if the probability of a value of the test statistic 'as bad or worse' as that obtained is p, then we reject that null hypothesis when p is less that or equal to the significance level.

How to decide whether one-tailed or two-tailed test is suitable?
-one-tailed:
is suitable for testing whether the parameter of the alternative hypothesis is greater than or less than the parameter of the null hypothesis.
-two-tailed:
is suitable for testing whether the parameter of the alternative hypothesis is different from the parameter of the null hypothesis.


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