2. xSampling Distribution ofSampling Distribution of
Introduction to Sampling DistributionsIntroduction to Sampling Distributions
Point EstimationPoint Estimation
Simple Random SamplingSimple Random Sampling
3. Statistical InferenceStatistical Inference
1. A1. A populationpopulation is the set of all theis the set of all the
elements of interest Eg- Mobile Phoneelements of interest Eg- Mobile Phone
usersusers
2. A2. A samplesample is a subset of the populationis a subset of the population
Eg- SAMSUNG mobile phone usersEg- SAMSUNG mobile phone users
4. 1 . Finite populations are often you know the
population:
• Organization membership roster
• Credit card account numbers
• Inventory product numbers
2. A2. A simple random sample of sizesimple random sample of size nn from a finitefrom a finite
population of sizepopulation of size NN..
Also you can say n/N x 100
5. 1. Infinite populations are often defined by an ongoing
process whereby the elements of the population consist
of items generated as though the process would operate
indefinitely.
2. A2. A simple random sample from an infinite populationsimple random sample from an infinite population
is a sample selected such that the following conditionsis a sample selected such that the following conditions
are satisfied.are satisfied.
• Each element selected comes from the sameEach element selected comes from the same
population.population.
• Each element is selected independently.Each element is selected independently.
6. 2. The random number selection procedure cannot be2. The random number selection procedure cannot be
used for infinite populations.used for infinite populations.
1. In the case of infinite populations, it is impossible to1. In the case of infinite populations, it is impossible to
obtain a list of all elements in the population.obtain a list of all elements in the population.
7. Point EstimationPoint Estimation
x
1. In1. In point estimationpoint estimation we use the data from the samplewe use the data from the sample
to compute a value of a sample statistic that servesto compute a value of a sample statistic that serves
as an estimate of a population parameter.as an estimate of a population parameter.
2. We refer to2. We refer to as theas the point estimatorpoint estimator of the populationof the population
meanmean µµ..
3. s3. s is theis the point estimatorpoint estimator of the population standardof the population standard
deviationdeviation σσ..
4. p is the4. p is the point estimatorpoint estimator of the population proportionof the population proportion pp..
8. Sampling ErrorSampling Error
The sampling errors are:The sampling errors are:
| |p p−2. For sample proportion2. For sample proportion
| |s σ−3. for sample standard deviation3. for sample standard deviation
| |x µ−1. For sample mean1. For sample mean
9. 900 applications annually from
prospective students. The
application form contains
a variety of information
including the individual’s
aptitude test score and whether or not
the individual desires on-campus housing.
10. The admissions would like to know the
following information:
• the average score for
the 900 applicants, and
• the proportion of
applicants that want to live on campus.
11. You can do as follows.
1Conducting a census of the entire 900 applicants
2. Selecting a sample of 30 applicants
12. 990
900
ix
µ = =
∑
2
( )
80
900
ix µ
σ
−
= =
∑
648
.72
900
p = =
1.Mean Score1.Mean Score
2.Population Standard Deviation for SAT Score2.Population Standard Deviation for SAT Score
3.Population Proportion Wanting On-Campus Housing3.Population Proportion Wanting On-Campus Housing
13. A Sample of 30 Applicants
• Because the finite population has 900 elements, weBecause the finite population has 900 elements, we
will need 3-digit random numbers to randomlywill need 3-digit random numbers to randomly
select applicants numbered from 1 to 900.select applicants numbered from 1 to 900.
14. Taking a Sample of 30 ApplicantsTaking a Sample of 30 Applicants
•The you can select 30 students for the sample.The you can select 30 students for the sample.
• For example, Excel’s functionFor example, Excel’s function
= RANDBETWEEN(1,900)= RANDBETWEEN(1,900)
can be used to generate random numbers betweencan be used to generate random numbers between
1 and 900.1 and 900.
Simple Random Sampling: Using EXELSimple Random Sampling: Using EXEL
15. 1. as Point Estimator of1. as Point Estimator of µµx
3. as Point Estimator of3. as Point Estimator of ppp
29,910
997
30
ix
x
n
= = =
∑
2
( ) 163,996
75.2
1 29
ix x
s
n
−
= = =
−
∑
20 30 .68p = =
2. s2. s as Point Estimator ofas Point Estimator of σσ
16. TheThe sampling distribution ofsampling distribution of is the probabilityis the probability
distribution of all possible values of the sampledistribution of all possible values of the sample
mean .mean .
x
x
Sampling Distribution ofSampling Distribution of x
where:where:
µµ = the population mean= the population mean
EE( ) =( ) = µµx
xExpected Value ofExpected Value of
17. Sampling Distribution ofSampling Distribution of x
1.Finite Population1.Finite Population 2. Infinite Population2. Infinite Population
σ
σ
x
n
N n
N
=
−
−
( )
1
σ
σ
x
n
=
• is referred to as theis referred to as the standard error of thestandard error of the
meanmean..
σx
• A finite population is treated as beingA finite population is treated as being
infinite ifinfinite if nn//NN << .05..05.
• is the finite correction factor.is the finite correction factor.( ) / ( )N n N− −1
xStandard Deviation ofStandard Deviation of
