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Maths > statistics > Flashcards

statistics Flashcards

1
Q

what is a census

A

measures every member of a population

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2
Q

advantage of a census

A

accurate results

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3
Q

disadvantage of a census

A

expensive / testing may destroy the population

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4
Q

what is a sampling unit

A

individuals of a population

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5
Q

what is a sampling frame

A

a list of sampling units

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6
Q

what is simple random sampling

A

same chance of being selected.
random number generator

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7
Q

advantage of simple random sampling

A

bias free

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8
Q

disadvantage of simple random sampling

A

need a sampling frame

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9
Q

what is systematic sampling

A

take every k’th unit. k=pop/sample
pick random number between 1 and k to start

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10
Q

advantage of systematic sampling

A

quick to use

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11
Q

disadvantage of systematic sampling

A

need a sampling frame

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12
Q

what is stratified sampling

A

sample represents the groups (strata) of a population.
sample/population x strata
to find out how many people you need in each group

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13
Q

advantage of stratified sampling

A

reflects population

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14
Q

disadvantage of stratified sampling

A

population must be classified in strata

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15
Q

what are strata

A

groups

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16
Q

what is quota sampling

A

like stratified but strata is filled by interviewer/researcher

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17
Q

advantages of quota sampling

A

no sampling frame

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18
Q

disadvantages of quota sampling

A

non random, potential bias

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19
Q

what is opportunity sampling

A

quota filled by those available at the time

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20
Q

advantages of opportunity sampling

A

easy/cheap

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21
Q

disadvantages of opportunity sampling

A

unlikely to be representative

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22
Q

how to calculate the variance

A

(sum of x^2 / n) - mean ^2
mean of the squares minus the square of the mean

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23
Q

go to get from variance to standard deviation

A

square root variance = standard deviation

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24
Q

why are histograms used

A

for continuous data

25
Q

what to compare on histograms

A

measure of location and measure of spread

26
Q

what does PMCC mean

A

product moment correlation coefficient

27
Q

what does PMCC measure

A

strength and +/- of correlation

28
Q

what is a regressions line

A

the best line of best fit

29
Q

what is interpolation

A

estimating inside the data range
more reliable

30
Q

what is extrapolation

A

estimating outside the data range
less reliable

31
Q

what is U on venn diagrams

A

shade all of both

32
Q

what is n on venn diagrams

A

shade overlap

33
Q

what does B| A mean

A

probability of B given that A has been picked

34
Q

what is a mutually exclusive event and its properties

A

the venn diagram does not overlap
P(AnB) = 0
P (AUB) = P(A) + P(B)

35
Q

probabilities of independant events on venn diagrams

A

P(AnB)= P(A) x P(B)
P(A|B) = P(A)

36
Q

conditional probability formula

P(B|A) =

A

P(AnB)/P(A)

37
Q

Addition law for probability

P(AUB) =

A

P(A) + P(B) - P(AnB)

38
Q

what is discrete uniform distributions

A

probabilities of all outcomes are equal

39
Q

Binomial distribution notation

A

X~B(n,p)
X is distributed binomials
n = number of trials
p = probability of success

40
Q

when to use a binomial distribution

A

F - fixed number of trials
F - fixed probability of success
I - independent
T - Two outcomes

41
Q

cumulative probability of P(X<5)

A

P(X<_ 4)

42
Q

cumulative probability of P(X>3)

A

1 - P(X<_3)

43
Q

cumulative probability of P(6<X<_10)

A

P(X<_10) - P(X<_6)

44
Q

what is normal distribution

A

used for continuous random variables

45
Q

normal distribution notation

A

Y ~ N (mean , variance)
y is distributed normally

46
Q

what are the points of inflection on normal distribution

A

mean + /- standard deviation

47
Q

what is the notation of standard normal distribution

A

Z~N(0, 1^2)

48
Q

coding Z~
Z=

A

Y-mean/standard deviation

49
Q

when can you approximate binomial distributions as normal distributions

A

if N is large
if p is approximately 0.5
mean = np
variance = np(1-p)

50
Q

if you are approximating binomial as normal you are going from discrete to continuous values so you must change the values of the probability.

e.g. P(X>5)

A

= P(Y> 4.5)

51
Q

what is the null hypothesis

A

H0 what we assume to be true

52
Q

what is alternative hypothesis

A

H1 what would be true if H0 is wrong

53
Q

what is significance level

A

the given threshold of likeliness

54
Q

what is a one tailed test

A

H1 : p>k or p<k

55
Q

what is a two tailed test

A

when H1 : p does not equal k
half significance level for each end

56
Q

for correlation testing what is
H0
and
H1
compare r with table for
more extreme
less extreme

A

H0: r=0
H1= r>0 or r<0 or r is not 0
if more extreme reject H0
is less extreme no evidence to reject H0

57
Q

for binomial testing what is
test statistic
H1
H0
assume H0 is

A

test statistic : number of successes observed
H0: p=k
H1 = p>k p<k p is not k
X~B(n,k)
find P(x<_>_ value in question)
if p< significance level - reject H0
if p> significance level - no evidence to reject H0</_>

58
Q

for normal testing what is
sample mean
H0
H1
assume H0 is

A

sample mean ~ N ( mean, variance/n)
H0 : mean = k
H1: mean > k mean < k or mean is not K
assume sample mean ~N ( k, variance/n)
find P(sample mean > or < mean of sample taken)
if p<significance level - reject H0
if p > significance level - no evidence to reject H0

59
Q
A

Maths (3 decks)

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