Statistics key words and definitions

Edexcel specification for S2- Ayomide OlubummoStatistics key words and definitionsWhen is a binomial distribution a suitable model for a practical solutionWhen there are only two outcomes-either success or failureThe probability of success remains constant.There are a fixed number of trials.The outcomes are independent of each otherHot tip: relate theses reasons to the situation given for the full marksWhen is a poisson distribution a good model to use.When event occurs at a constant rate They occur singlyThey are independent of each other ( so in cases of catching fishes or other organisms, you assume that the fishes location is completely random and independent of other fishes which is not always the case.Hot tip; Again relate this to the context givenHow do you know when to use the Poisson distribution as an approximation to the binomialWhen n is large When p is smallWhen to apply the continuity correction You apply the continuity correction when moving from a discrete distribution to a normal one. This is the case when approximation from either the binomial or Poisson to the normal as the normal is continuous while the binomial and Poisson is discrete.This involves +/- 0.5 depending on whether or not you want to keep the observed value (X)When would you use the normal distribution to approximate a binomialN is large P is close to 0.5When would you use the Poisson to approximate the normal When lamba ( ) is large

What is meant by a population A collection of individual items and people

What is the difference between a census and a sampleA census is information collected from ALL members of the populationA sample is information collected from CHOSEN members of the population.

What is meant by a sampling frameA numbered list of all the sampling units in the population.For example if you where collecting information about the school from student using a class as a sample you would use the class register as a sampling frame as it has a numbered list of all the sampling units ( see the next slide) in this case students.

What is meant by a sampling unitThe individual units in the population.So again if you were collecting information from a school, the students would be the sampling units. A numbered list of the students would then form the sampling frameWhat are the advantages of taking a censusAll the members of the population surveyed therefore representative.UnbiasedLike to get more accurate data

What are the disadvantages of doing s censusCostlyTime consuming Hard to ensure all the members of the population are surveyedWhat is a sampling distribution of a statistic Firstly a statistic is a quantity calculated from observations so there are no unknown parameters.A sampling distribution contains all the values of the statistic and the probability that each will happen by chance alone.What is an hypothesisA statement about the population parameterWhat is an hypothesis testA mathematical procedure that evaluate the value of the population parameter proposed by the null hypothesis by comparing it to the alternative hypothesisWhat is meant by the null hypothesisWhat we assume is correct. H0

What is the alternative hypothesis Tells us about population parameter if our assumption is shown to be wrong.When to use one or two tailed testsOne tailed when want to test whether it can increased or decreased.Two tail when you want to test change in proportion.What is meant by a critical regionThe range of values that would lead to a significant test thus the rejection of the null hypothesis and acceptance of the alternative hypothesis.Hot tip: always split the level to calculate the significance figure unless told otherwise in the question.What is meant by the significance levelThe probability of incorrectly rejecting the null hypothesis.Calculated by adding the probabilities of the boundaries of the critical region