# 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?

#### Back

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

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