# stats 2

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• Created by: Ellie
• Created on: 14-04-15 10:01
Using the binomial what is the probability of (x=x)?
ncx p^x (1-p)^(n-x)
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How do you work out the expected value given the binomial?
E(x)= np
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How do you work out the variance given the binomial?
V(x) = np(1-p)
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Using the poisson what is the probability of (x=x)?
λ^x/x! times e^-λ
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What is the expected value and variance in a poisson distribution?
E(x)= λ V(x)=λ
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What is the sum of two independent poisson variables?
z~p(λ+μ)
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How do you find λ when doing a poisson approximation to the binomial?
λ=np
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How do you find the probability of x < x in the normal distribution?
ф(x-μ/σ)
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How do you write the normal distribution?
X~N(μ,σ^2)
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When do you need a continuity correction when using the normal distribution?
when you are doing an approximation to the binomial
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What is the continuity correction of p(x
P(x
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What is the continuity correction of p(x
p(x
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What is the continuity correction of p(x>=3)?
p(x>2.5)
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What is the continuity correction of p(x>3)?
p(x>3.5)
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What is the continuity correction of p(x=5)?
p(4.5
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What is the continuity correction of p(3
p(2.5
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What is the continuity correction of p(3
p(3.5
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What is the normal statistic when doing an approximation to the binomial?
X~N(np,np(1-p))
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What is the normal statistic when doing an approximation to the poisson?
X~N(λ,λ)
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When do you do a binomial approximation to the poisson?
When n is large and p is small (
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When do you do a binomial approximation to the normal?
When n is large and p is near 0.5
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When do you do a poisson approximation to the normal?
when λ>10
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What are the conditions of a poisson distribution?
Events must occur randomly, uniformly (at the same rate), independently and in a fixed space or time.
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When doing a chi^2 distribution what is the nul hypothesis?
H0: there is no association between....
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How do you work out the x^2 value?
the sum of (oi-ei)^2/ei
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What are the degrees of freedom?
The number of independent values(the ones you worked out not by subtraction)
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What do the numbers in the x^2 table show you?
The difference between oi and ei
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What is the normal distribution of a sample mean?
x̄~N((μ,σ/square root of n)
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Describe the steps required to do a hypothesis test of the sample mean
1. Define population mean μ in context. 2. Define the random variable x. 3. State Ho: μ= and H1: μ 4. Find the significance level and type of test. 5.Find the test statistic using tables 6. Find the critical value
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How do you work out the PMCC?
r= sxy/ square root(sxx . syy)
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How do you work out sxx?
Σx^2-nx̄^2
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How do you work out syy?
Σy^2-nybar^2
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How do you work out sxy?
Σxy-nx̄ybar
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If r=1 what type of correlation is there?
perfect positive correlation
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If r=-1 what type of correlation is there?
perfect negative correlation
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How do you do a PMCC to Normal distribution hypothesis test?
1. State ρ(parent population) 2. State Ho: ρ= and H1: ρ 3. State the significance level 4. Find the critical value in tables 5. State critical region 6. Calculate PMCC 7. conclude
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What does a PMCC to Normal distribution test assume?
That both variables are random and the scatter diagram gives an approximate elliptical distribution.
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What is important to know about correlation?
Correlation does not imply causation
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What is the first step in spearmans rank?
Rank your x and y values from 1 to n then work out the difference
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How do you work out spearmans rank?
1- 6Σdi^2/(n(n^2-1))
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What must a line of best fit always go through?
xbar, ybar
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How can you work out the equation of a regression line?
y-ybar=bhat(x-xbar)
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How do you work out b hat?
sxy/sxx
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## Other cards in this set

### Card 2

#### Front

How do you work out the expected value given the binomial?

E(x)= np

### Card 3

#### Front

How do you work out the variance given the binomial?

#### Back ### Card 4

#### Front

Using the poisson what is the probability of (x=x)?

#### Back ### Card 5

#### Front

What is the expected value and variance in a poisson distribution?

#### Back ## Comments

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