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Quantitive Methods > Lecture Six > Flashcards

Lecture Six Flashcards

1
Q

What is the purpose of statistical inference

A

to obtain information about a population from information contained in a sample

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2
Q

What is population

A

the set of ALL elements of interest

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3
Q

What is a sample

A

a subset of the population

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4
Q

What do the sample results provide

A

only ESTIMATES of the values of the population characteristics

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5
Q

What can proper sampling methods do

A

sample returns can provide GOOD estimates of the population characteristics

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6
Q

why do we work with samples

A

in statistical inference it is too costly in terms of time and money to work in the population

-more easier & more efficient
-costly and sometimes not possible
-e.g. the census it is a huge amount of money and time implemented to check every single person in the population
=to reduce time and effort work the sample

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7
Q

what is the true value

A

population

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8
Q

What is the idea when working with samples

A

-idea is to get the inference closes to the population (true value)
-its important for decisions made

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9
Q

Why do we work with random sampling

A

-to avoid bias
-allows probability to make inferences about unknown population parameters (e.g. mean/variance).
-only if they are random otherwise no basis for using probability to make this inference

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10
Q

What is the reason for the probability when working with random variables

A

-what is the probability that the estimate of the sample variance is the estimate

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11
Q

What shape is the population data graph

A

a bell shape

-e.g. selecting the first 1000 for the sample then the next 1000 and etc – the first second and last part

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12
Q

what happens with the sample graph shape if it is accurate

A

when properly take a sample = resembles the population shape

-if shape is similar get close values

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13
Q

what happens with the sample graph shape if it is not accurate

A

-when there’s mistakes – doesn’t represent the entire section
-not shaped similar to the population

-the shape would be different = values are not the same to the population

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14
Q

what is meant by arbitrary sampling

A

a non-random sampling method where units are selected in a haphazard manner, with little or no planning.

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15
Q

Why is arbitrary sampling bad

A

Arbitrary sampling is biased, and the results are speculative

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16
Q

What would a arbitrary sample graph look like

A

different - not similar to the population = inaccurate representation

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17
Q

Finite population defined by? and examples

A

often defined by lists:
-organisation membership roster
-credit card account numbers

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18
Q

what happens when a simple random sample size of n from a finite population of size N

A

is the sample selected such that each possible sample of size n has the same probability of being selected

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19
Q

What is sampling with replacement

A

replacing each sampled element before selecting subsequent elements

-procedure used most often

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20
Q

is finite population bias

A

yes

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21
Q

What are infinite populations defined by

A

an ongoing process where the elements of the population consist of items generated as though the process would operate indefinitely

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22
Q

what are the conditions when selecting a simple random sample from an infinite population

A

-each element comes from the SAME population
-each element is selected independently

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23
Q

is it easy to get all of the elements in population for a infinite population

A

no, it is impossible to obtain a list of ALL elements in the population

-e.g. human ppl die ppl born – numbers constantly changing
=impossible to track values

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24
Q

can random number selection procedure be used for infinite population

A

no.

25
Q

how is simple random sampling chosen

A

chosen by a process that selects a sample of n objects from a population in such a way that each member of a population has the same probability of being selected

26
Q

find the simple random sample if population size is N=5, and we want a sample size of n=2

A

Total number of pairs we can have are (5,2) = 10
-therefore each pair has a probability of 1/10

-can use Uniform distribution: Unif(1,10) where 1 and 10 are the upper and lower limit

27
Q

what does systematic sampling do

A

provide a convenient way to choose a random sample as every kth member is selected from a list/other ordering

28
Q

what is the systemtic sampling when population N=55000 (names listed in alphabetical order) and we want a random sample of n = 250 names,

A

systematic sampling would select every k = N/n member of the population = 55000/250 = 220

-there are 220 different possible samples - depending on the first number chosen = each is equal likely

29
Q

an examples of when businesses may use systematic sampling

A

when businesses are auditing - they need to chose at random companies to audit

29
Q

an example of stratified sampling

A

to obtain a stratified random sample acorrding to age - small age groups can be formed
-first group (0-5)
-second group (6-10)
-third group (11-15)
-fourth (16,20) etc.

once groups identified - each group is formed by using the simple random sample approach

29
Q

what is the stratified sampling

A

if condition is unevenly distributed in a population with respect to age, gender or some other variable

30
Q

where are stratified sampling common in

A

portfolio managers, hedge funds

=e.g. very risky stocks represents the group/ liquid stocks
-having liquid stock – need a premium to hold the stock to get a larger return (

31
Q

what is meant by point estimation

A

use data from the sample to compute a value of a sample statistic that serves as a estimate of a population parameter

32
Q

what do we refer to as the x with the line ontop

A

point estimator of the population mean - mew

33
Q

What is Sx in the point estimator contect

A

Sx = point estimator of population standard deviation

34
Q

what is p with line ontop

A

point estimator of population proportion p

35
Q

when is the point estimator unbiased

A

when the expected value of a point estimator is equal to the population parameter

36
Q

What are the two sources of errors that can occur when sampling randomly from a population

A

sampling error and non sampling error

37
Q

what is the sampling error

A

inevitable result of basing an inference on a random sample rather then on the entire population non sampling error

38
Q

when does the non response bias occur

A

when a portion of the sample fails to respond to the servey

39
Q

when does measurement error occur

A

when the responses to the question do not reflect what the investigator has in mind
-when the variables considered are estimates rather then true values

40
Q

what is the sample error for the sample mean (equation)

A

x (with line ontop) − μ

41
Q

what is the sample error for standard deviation

A

SX − σ

42
Q

what is the sample error for sample proportion

A

p(with line ontop) − p

43
Q

sample mean of random variables is

A

sum of all observations over 1/n

44
Q

what type pf distribution can x be

A

normal , uniform or any type

45
Q

what should the sample mean equal to

A

the population mean

46
Q

what happens to the sample variance if n increases

A

the variance shrinks - closer to 0

47
Q

what is true data

A

population data,

48
Q

how does sample data become closer to the true value

A

-needs a huge amount of data = the true value
-more data = more true

49
Q

what is the standard error

A

sqrt(sample v/n)

50
Q

what changes the value of the standard error

A

more values in the sample data

51
Q

how to know if sample members are independently distributed of one another

A

if sample size n is not a small fraction of the population size N

52
Q

what is the variance of sample mean if observations are not selected independently

A

variance / n times N-n/N-1

53
Q

what is the finite population correction factor

A

(N-n)/(N-1)

54
Q

when is finite population treated as infinite population

A

if n/N is smaller or equal to 0.05

55
Q

what must u assume about infinite and finite variance

A

always infinite

56
Q
A

Quantitive Methods (6 decks)

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