S2 flashcards

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What are the four conditions required for a binomial distribution?
A fixed number of trials (n), each trial should be success or failure, the trials are independent, the probability of each success (p) is constant
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X~B (n,p)
B for binomial, n for the number of trials, p for the probability of success
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E(X) of a binomial distribution
np (the mean)
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Var(X) of a binomial distribution
np(1-p) (the standard deviation of the distribution squared)
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If X is to have a Poisson distribution the events must occur?
singly in space or time, independently of each other, at a constant rate
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E(X) of a Poisson distribution
λ (the mean)
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Var(X) of a Poisson distribution
λ (standard deviation squared)
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What are the two conditions needed to be able to use the Poisson distribution as an approximation for the binomial distribution?
n is large, p is small, then X~B(n,p) can be approximated by Po(np)
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If a question mentions rate...
suggests a Poisson distribution
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If a question mentions a fixed number of trials or a proportion....
suggests a binomial distribution
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Is there a value for n?
use the binomial distribution
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Is there a constant probability of success?
use the binomial distribution
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Is there a rate of occurence of an average number of occurences?
use the Poisson distribution
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Can you say how many times something will not happen?
if yes, probably a fixed n and use the binomial, if no use a Poisson distribution
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If X is a continuous random variable with p.d.f. f(x) then...
f(x) is greater than or equal to 0, P(a
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How do you get from p.d.f. to c.d.f.?
integrate
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How do you get from c.d.f. to p.d.f.?
differentiate
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E(X) of a continuous random variable
∫xf(x)dx
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Var(X) of a continuous random variable
∫xsquaredf(x)dx-µ squared
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What is the mode of a CRV?
the value of the random variable where it is most dense i.e. where the p.d.f. reaches its highest point
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What is the median of a CRV?
F(m) = 0.5
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What is the lower quartile of a CRV?
F(Q1) = 0.25
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What is the upper quartile of a CRV?
F(Q3) = 0.75
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E(X) of a continuous distribution
a+b divided by 2
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Var(X) of a continuous distribution
(b-a) squared then divded by 12
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What are the two rules for continuity correction?
first write the probability using ≤ or ≥, for P(X≤n) use P(Y
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When can you use the normal distribution as an approximation for the binomial distribution?
n is large, p is close to 0.5, then X can be approximated by Y~N(np, np(1-p))
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X~Po(λ) can be approximated by...
Y~N(λ,(√λ) squared)
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What is a population?
a collection of individual people or items
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A population may be of...
finite size
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A population may be considered to be of infinite size if...
it is impossible to know exactly how many members there are in the population
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A population may be of countably infinite size if...
we know the population could be infinite but in practice we count thr number of individual members of it
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If information is to be obtained from all members of the population, the investigation is known as...
a census
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What are the advantages of taking a census?
every single member of the population is used, it is unbiased, it gives an accurate answer
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What are the disadvantages of taking a census?
it takes a long time to do, it is costly, it is often difficult to ensure that the whole population is surveyed
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the chosen members are called a...
sample
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an investigation using a sample is called...
a sample survey
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the individual units of a population are known as...
sampling units
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a list of sampling units are known as...
a sampling frame
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If a population is large and well mixed a sample will be...
representative of the whole population
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What are the advantages of a representative sample?
generally cheaper than taking a census, advantageous where the testing of items results in their destruction, data generally more readibly available
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What are the disadvantages of a representative sample?
uncertainity involving natural variation and bias
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What is a hypothesis?
a statement made about the value of a population parameter that we wish to test by collecting evidence in the form of a sample
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What is a test statistic?
a sample summarised in the form a statistic
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What is a null hypothesis?
the hypothesis we assume to be correct unless proved otherwise (H0)
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What is an alternative hypothesis?
tells us about the value of the population parameter if our assumption is proved to be wrong (H1)
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What is the critical region?
the range of values of the test statistic that would lead you to rejecting H0
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What is a critical value?
a value on the boundary of the critical region
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What is the level of significance?
a threshold probability, usually 5% or 1%, denoted by α
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A one-tailed test looks for either...
an increase or a decrease in the value of a parameter
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For a null hypothesis H0:θ=m, a one-tailed test is used when...
the alternative hypothesis is H1:θ>m or H1θ
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A one-tailed test will have...
a single part to the critical region and one critical value
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A two tailed test arises when...
the alternative hypothesis is H1:θ≠m
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If the test is two-tailed there will be...
two critical regions and two critical values
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If we have a 5% significance level the usual convention is...
to allow 2½% at either tail
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The actual level of significance of the test is...
the probability of rejecting H0
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Other cards in this set

Card 2

Front

B for binomial, n for the number of trials, p for the probability of success

Back

X~B (n,p)

Card 3

Front

np (the mean)

Back

Preview of the back of card 3

Card 4

Front

np(1-p) (the standard deviation of the distribution squared)

Back

Preview of the back of card 4

Card 5

Front

singly in space or time, independently of each other, at a constant rate

Back

Preview of the back of card 5
View more cards

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