Question

"given a population in which the probability of success is p = 0.20, if a sample of 500 items is taken, then calculate the probability the proportion of successes in the sample will be between 0.18 and 0.23 if the sample size is 200."

Answer 1

Binomial conditionsfixed number of trials
each trial must be either a success or a fail
trails must be independent
the value of P must remain constantBinomial E(X)npBinomial Var(X)np(1-p)Poisson conditionsevents must be independent
events must occur singly in space or time
event must occur at a constant ratepoisson E(X)£Var(X)£binomial to normaln is large
p is close to 0.5
N(np,np(1-p)
np>10binomial to poissonn is large
p is small
Po(np)
np<10poisson to normaln is large
N(£,£)populationa collection of itemscensusinformation obtained from every member of a populationsamplea selection of indvidual members from a populationpopulation parameterany characteristic of a population which is measurablefinite populationa population in whihc every individual member can be given a numberinfinite populationa population which is impossible to give a number to every individualadvantage censusevery single member of a population is used, unbiased, gives an accurate answerdisadvantage censustime consuming, costly, difficult to ensure that the whole population is surveyeddisadvantage samplenatural variation
biasadvantage samplesample is representative
cheaper
data more readily avaliblepoissonevents occur randomly
singly in space or time
independently of each other
constant ratebinomialfixed number of trials
each trail either a success or failure
trails independent
probability of success constantsignificance levelprobability of incorrectly rejecting the null hypothesisstatisticrandom variable quantity calculated soley from observations in a sample does not involve any unknown parameters numerical property of a samplesampling distributionall possible values of a test statistic and their probabilitiessampling framea list of all the sampling units within a populationsampling unitsthe individual units of a populationsample surveyan investigation using a samplerandom samplingevery possible sample of size n has an equal chance of being selectedhypothesisa statement made about the value of a population parameternull hypothesishypothesis that is assumed to be correcttest statistica form of a statistic in which the evidence from a sample in a hypothesis test is summarisedcritical valuesthe values on the boundaries