Lecture Six

Question 1

What is the purpose of statistical inference

Answer 1

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

Question 2

What is population

Answer 2

the set of ALL elements of interest

Question 3

What is a sample

Answer 3

a subset of the population

Question 4

What do the sample results provide

Answer 4

only ESTIMATES of the values of the population characteristics

Question 5

What can proper sampling methods do

Answer 5

sample returns can provide GOOD estimates of the population characteristics

Question 6

why do we work with samples

Answer 6

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

Question 7

what is the true value

Answer 7

population

Question 8

What is the idea when working with samples

Answer 8

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

Question 9

Why do we work with random sampling

Answer 9

-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

Question 10

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

Answer 10

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

Question 11

What shape is the population data graph

Answer 11

a bell shape

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

Question 12

what happens with the sample graph shape if it is accurate

Answer 12

when properly take a sample = resembles the population shape

-if shape is similar get close values

Question 13

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

Answer 13

-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

Question 14

what is meant by arbitrary sampling

Answer 14

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

Question 15

Why is arbitrary sampling bad

Answer 15

Arbitrary sampling is biased, and the results are speculative

Question 16

What would a arbitrary sample graph look like

Answer 16

different - not similar to the population = inaccurate representation

Question 17

Finite population defined by? and examples

Answer 17

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

Question 18

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

Answer 18

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

Question 19

What is sampling with replacement

Answer 19

replacing each sampled element before selecting subsequent elements

-procedure used most often

Question 20

is finite population bias

Answer 20

yes

Question 21

What are infinite populations defined by

Answer 21

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

Question 22

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

Answer 22

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

Question 23

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

Answer 23

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

Question 24

can random number selection procedure be used for infinite population

Answer 24

no.

Question 25

how is simple random sampling chosen

Answer 25

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

Question 26

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

Answer 26

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

Question 27

what does systematic sampling do

Answer 27

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

Question 28

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

Answer 28

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

Question 29

an examples of when businesses may use systematic sampling

Answer 29

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

Question 29

an example of stratified sampling

Answer 29

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

Question 29

what is the stratified sampling

Answer 29

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

Question 30

where are stratified sampling common in

Answer 30

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 (

Question 31

what is meant by point estimation

Answer 31

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

Question 32

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

Answer 32

point estimator of the population mean - mew

Question 33

What is Sx in the point estimator contect

Answer 33

Sx = point estimator of population standard deviation

Question 34

what is p with line ontop

Answer 34

point estimator of population proportion p

Question 35

when is the point estimator unbiased

Answer 35

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

Question 36

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

Answer 36

sampling error and non sampling error

Question 37

what is the sampling error

Answer 37

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

Question 38

when does the non response bias occur

Answer 38

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

Question 39

when does measurement error occur

Answer 39

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

Question 40

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

Answer 40

x (with line ontop) − μ

Question 41

what is the sample error for standard deviation

Answer 41

SX − σ

Question 42

what is the sample error for sample proportion

Answer 42

p(with line ontop) − p

Question 43

sample mean of random variables is

Answer 43

sum of all observations over 1/n

Question 44

what type pf distribution can x be

Answer 44

normal , uniform or any type

Question 45

what should the sample mean equal to

Answer 45

the population mean

Question 46

what happens to the sample variance if n increases

Answer 46

the variance shrinks - closer to 0

Question 47

what is true data

Answer 47

population data,

Question 48

how does sample data become closer to the true value

Answer 48

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

Question 49

what is the standard error

Answer 49

sqrt(sample v/n)

Question 50

what changes the value of the standard error

Answer 50

more values in the sample data

Question 51

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

Answer 51

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

Question 52

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

Answer 52

variance / n times N-n/N-1

Question 53

what is the finite population correction factor

Answer 53

(N-n)/(N-1)

Question 54

when is finite population treated as infinite population

Answer 54

if n/N is smaller or equal to 0.05

Question 55

what must u assume about infinite and finite variance

Answer 55

always infinite