Statistical Interference

Question 1

Population

Answer 1

A wide set of data which is of interest - whether we are referring to measurements on people, animals or things

The electorate
Potential customers
Retail prices
Invoices issued by a company

Question 2

Sample

Answer 2

We use a sample of data to infer something about the population from which it came

Opinion poll
Market research survey
Retail price index
Audit sample

Question 3

Types of sample

Answer 3

Simple random sampling - every possible sample size has an equal chance of being selected (raffle tickets)
Requires a list of every item in the population (sampling frame)

Cluster sampling -population may naturally occur in clusters e.g. Families,post codes, students in schools, streets

Cluster sampling selects a sample of the clusters

Stratified sampling -divide the population into groups or strata e.g. Gender, regions take a sample from each one e.g. 10%

Convenience sampling used uses the individuals it is easiest to find

Question 4

Ads and dis ads of Stratified sampling

Answer 4

Ad-
ensures all groups are represented
Can study each stratum separately
Separate lists may be available for each stratum

Dis
Method of analysis is more complicated

Question 5

Ads and dis ads of cluster sampling

Answer 5

Ads
May be cheaper (some post codes only to cut travel costs)
Don’t need list of whole population

Dis
Analysis more complicated than simple random sample
Individuals in a cluster may be similar so may need bigger samples for the same degree of precision as a simple random variable

Question 6

Population and sample letters

Answer 6

U= pop mean
Ō^2 = pop variance
_
X=sample mean 
S^2= sample variance 

_
X and s^2 are calculated from the sample and are estimators of U and ō^2w

Question 7

Sample mean and sample variance

Answer 7

Mean

_
X = Ex/n

Variance = E(x-X)^2/n-1

_
X = X ^^^

Sample mean is used to measure pop mean
Sample variance is used to measure poo variance

Question 8

Standard error

Answer 8

_
Variance of sample mean,(x) is Ō^2/n

Standard deviation of sample mean is
Square root of Ō^2/n or ō/ square route (n)

Standard deviation of estimator statistic like _
X
Is standard error
It gives some idea of the accuracy of using sample mean to estimate the pop mean

Question 9

Probability statements about the mean

Answer 9

95% of sample lies between 2 standard errors of the population mean

Nearly all of sample means lie within three standard errors of the population mean

Applies even if data does not have normal distribution