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OCR MEI statistics > S2 > Flashcards

S2 Flashcards

0
Q

What is the formula for the Poisson distribution?

A

P(x=r)= e^-λ X (λ^r/r!)

λ is the mean no. of times something happens and r is the number of things that could happen.

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1
Q

When can the Poisson distribution be used?

A

The events occur at random and independently of each other.

The average number of events is uniform and finite

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2
Q

What must you be sure of before you find the sum of 2 or more Poisson distributions?

A

Insure that they are independent of each other.

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3
Q

How is the variance of a large set of values found?

A

Find the total of x²f.
Square the mean and multiply by the total of xf
Minus the latter from the former.
Divide this by n-1

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4
Q

What is the formula to find z for the normal distribution?

A

(X-u)/ SD

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5
Q

What is the formula to find z for the normal distribution?

A

z= (X-u)/ SD

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6
Q

Why do we need to use continuity corrections when modelling with the normal distribution?

A

The normal distribution is continuous but we will use a discrete distribution(in the formal of the binomial distribution) to model it.

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7
Q

What must there be if we can model the binomial distribution with the normal?

A

N is large.
Probability must be near to 0.5
NP must be equal to or more than 10.

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8
Q

What does a capital X denote?

A

a distribution, It will have its own SD and mean.

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9
Q

What does a small x denote?

A

a particular value.

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10
Q

When approximating a binomial distribution with the normal, how is the mean found?

A

N times P

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11
Q

When approximating a binomial distribution with the normal, how is the SD found?

A

The varience is NP(1-P)
The SD is the square root of this. Remember when writing the notation for the normal distribution to square the sd as we always write the variance.

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12
Q

What does a capital x̅ or μ mean?

A

The mean of a whole distribution. The population mean.

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13
Q

what does a lower case x̅ mean?

A

The mean of a sample.

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14
Q

If you conduct a two tailed test and do a hypothesis test, what do you do?

A

Halve the significance level and carry on as normal.

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15
Q

When a sample is done from a population and their is a different mean, how is the SD of the new sample?

A

Divide the SD of the old sample by the square root of the number of variables in the sample.

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16
Q

How does method 3 work?

A

Find the test statistic or Z of the sample by subtracting the mean of the population from the mean of the sample and divide by the SD of the sample.
Use the inverse normal distribution tables with 1- the significance level.
If it is within the significance level, accept h1

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17
Q

Give some examples of things that can be modeled by the Poisson distribution.

A

No. of accidents in a factory every month.

Insurance claims made by motorists in a month.

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18
Q

How would you find P(X≥2) without using the Poisson distribution tables?

A

Use the formula to find the P of 0 and 1 and minus this from 1.

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19
Q

When using the Poisson to approximate the binomial distribution, how is λ found?

A

λ= N times P

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20
Q

If the question is one where you have to show that the answer is a given number, what do you do?

A

Calculate it to a greater no of significant figures to show your understanding.

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21
Q

If you have to calculate an expected value, in what form do you give your answer?

A

Give to 3 sf and state so and also state a rounded version.

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22
Q

What does state the distribution mean?

A

Give n and p.
If it was a binomial distribution it would be written in the form
X~B(n,p)

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23
Q

What is the notation for the Poisson distribution?

A

x ̴ Pₒ (λ) where λ is the mean.

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24
Q

What is the notation for the binomial distribution?

A

x ̴ B(n p)

25
Q

Is the normal distribution continuous or discrete?

A

continuous.

26
Q

When using the inverse tables for the normal distribution what must z be in relation to a?

A

x<a>a. If it is z>a change it to z<-b.</a>

27
Q

What is the notation with the normal distribution?

A

X ~ N (U, σ²) You have the square sign as you are writing the variance.

28
Q

When using the normal approximation to the Poisson, how is the mean and sd found?

A

The mean and variance will be equal to average used in the poisson. Remember the sd is the root of the varience.

29
Q

When testing for the mean, what are the two hypothesizes?

A

Hₒ :μ = population mean
H₁ : μ < or > or ≠ depending on the question.
Remember to write “ where μ is the population mean ….”

30
Q

When testing for the mean, how is the normal distribution for the sample found?

A

The mean is the mean of the population. The sd is the sd of the population divided by the root of the number in the sample.

31
Q

What do contingency tables tell you?

A

If 2 sets of data are independent or not.

32
Q

When doing the expected table of values in the contingency table questions how do you find them?

A

Find the total for each row and column and the total.
Then divide one of the column totals by the total total and multiply by the correct row total.
You can check to see if you are correct as the totals for the rows and columns should be the same.

33
Q

When doing the expected table of values in the contingency table questions how do you find the chi² values?

A

Subtract the expected value from the observed value and square this.
Then divide this by expected value.

34
Q

What do the chi squared values tell you?

A

The larger they are the greater it is from what you would expect.

35
Q

How do finish the contingency table questions?

A

Add all the values together and then use the tables. The degrees of freedom is one less than the number of rows times one less than the number of columns.

36
Q

On a scatter graph what goes on what axis?

A

On the x axis the independent value.

On the y axis the dependent value.

37
Q

What is a bi modal correlation?

A

One where there are 2 clusters of points.

38
Q

why in contingency tables are the values calculated the way they are?

A

We assume them to be independent, and we use totals to find probabilities. These we can multiply to give expected values.

39
Q

How do you find the PPMCC ?

A

Find Σx, Σy, Σxy, Σx² and Σy². Find the mean for x and y.
Find Sxx by Σx²-nx̄ ²and do the same for Syy
Find Sxy by doing Σxy-nx̄ybar
r= Sxy/(√(Sxx*Syy)

40
Q

What does ρ mean?

What does r mean?

A

PMCC for the parent population.

PMCC for the sample population.

41
Q

When doing a hypothesis test with the PPMCC what are the hypothesis?

A

Hₒ:ρ=0

H₁:ρ ≠ 0

42
Q

When doing a hypothesis test with the PPMCC, what must you say?

A

Where ρ is the correlation coefficient for the parent population.

43
Q

How is the equation of a least square regression line found?

A

y-ybar= (Sxy÷Sxx)*(x-x̄)

44
Q

When can you approximate the binomial distribution with poission?

A

When n is large (greater than 50) and p is small. ( less than 0.1)

45
Q

How do you find the critical value when testing for the mean?

A

If they gave you a significance level like 5 % go to the inverse normal function table and look for the value for 0.95.

46
Q

With spearmans rank, how do you know when to do a one tail or two tail test?

A

Two tail test if you want to know if there is an association or no association,
One tail test if you want to know if there is no association or a positively negative one.

47
Q

What are the conditions needed to approximate the poission distribution with normal?

A

λ should be at least 10 or large generally. This is because the larger λ is the more the Poisson distribution looks like a continuous one.

48
Q

If a scatter graph gives an oval shape, what does that mean?

A

The there is a biverate normal distribution shown.

49
Q

If you do a sample and the scatter graph of it shows a correlation of sorts, do you do a one or 2 tail test?

A

The hypothesis shouldn’t be determined by the sample data and they should be a suggestion if it is positive or negative for it to be one tail.

50
Q

What does ⍴ mean ?

A

The linear correlation coefficient of a population.

51
Q

What point must the least square regression line go through?

A

The mean of x and the mean of y. (Xbar, Ybar,)

52
Q

How do the residuals play in obtaining the equation for the regression line?

A

The line is made to minimise the sum of the squares of the regressions.

53
Q

What is an out liar?

A

2sd away from the mean or 1.5*IQR from the upper or lower quartile, not from the median.

54
Q

When doing a chi squared test, what are the hypothesis?

A

Write both out in full. H0 the two variables are independent in the population.
H1 the two variables are not independent in the population.

55
Q

When doing spearmans rank, what are the hypothesis?

A

H0 there is no association between the 2 variables in the population.
H1 there is an association between the 2 variables in the population.

56
Q

When using the inverse normal distribution tables and you know the probability of something being less or more than a value is less than 0.5, what do you do?

A

Make a -a

57
Q

When using the inverse normal distribution tables, what must z be in relation to a?

A

Z must be less than a . If is it greater than, change the probability by subtracting it from 1 and using that.

58
Q

What is the significance level?

A

The probability of rejecting the null hypothesis when it is true.

59
Q

What must the least square division line be in terms of?

A

Not x and y. If you were comparing weight and height, you would use w and h instead.

60
Q

How by is a residual found?

A

Use the equation of your line to find the value you would expect at that point. Subtract the expectation from the true. Keep it negative if you need to.

OCR MEI statistics (4 decks)

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