STAT3
STAT3
STAT3
AND
PROBABILITY
PARAMETER STATISTICS
SAMPLING TECHNIQUES
• SAMPLING – process of selecting sample
• RANDOM SAMPLING – process whose members
had an equal chance of being selected from the
population
• NON – RANDOM SAMPLING – a sampling
procedure where samples are selected in a
deliberate manner with little or no attention to
randomization
RANDOM SAMPLING
1. SIMPLE – process of selecting n sample size in the
population via random numbers or through lottery
2. SYSTEMATIC – process of selecting kth element in the
population until the desired number of subjects is attained
3. STRATIFIED – process of subdividing the population
into subgroups or strata and drawing members at random
from each subgroup
4. CLUSTER – process of selecting clusters from a
population which is very large
NON – RANDOM SAMPLING
1. CONVENIENCE – process of selecting a group of individuals who are
available for study
2. PURPOSIVE / JUDGMENT – process of selecting based from judgment
to select a sample which the researcher believed, based on prior
information, will provide the data they need.
3. QUOTA – applied when an investigator survey collects information from
an assigned number
4. SNOWBALL – technique in which one or more members of a population
are located and used to lead the researchers to other members of the
population
5. VOLUNTARY – technique when sample are composed of respondents
who are self – select into the study/survey
SAMPLING DISTRIBUTION OF SAMPLE
MEANS
• SAMPLING WITH REPLACEMENT
• SAMPLING WITHOUT REPLACEMENT
• FINITE POPULATION
• INFINITE POPULATION
• COMBINATION
CHARACTERISTICS OF SAMPLING
DISTRIBUTION
•
1. STANDARD ERROR
Liza 1
Kathryn 2
Julia 3
Sofia 4
Riana 5
Janina 6
A.What is the population mean, population
variance, and population standard deviation
of the given data?
B.What is the sampling distribution of the
sample means for a sample of size 2?
C.What is the mean, variance, and standard
deviation of the sampling distribution?
D.What observation can be made with respect
to the population and the sampling
distribution?
EMPLOYEES YEARS IN THE BUSINESS (x)
Liza 1
Kathryn 2
Julia 3
Sofia 4
Riana 5
Janina 6
•
YEARS IN THE
EMPLOYEES
BUSINESS (x)
𝑥−𝜇
( 𝑥 − 𝜇 )2
Liza 1 − 2.5 6 .25
2 𝞢 ( 𝑥 − 𝜇)2 2 17.50
𝜎 = 𝜎 = =𝟐 .𝟗𝟐
𝑁 6
2
𝞢(𝑥 − 𝜇)
𝜎=
√
𝑁
𝜎 =√ 2.92=𝟏. 𝟕𝟏
STEP 1. Find the number of possible samples.
•
STEP 2.List all possible samples.
OBSERVATION EMPLOYEES YEARS
1 Liza , Kathryn 1,2
2
Liza , Julia 1,3
3
Liza , Sofia 1,4
4
5 Liza , Riana 1,5
6 Liza , Janina 1,6
7 Kathryn , Julia 2,3
8 Kathryn , Sofia 2,4
9 Kathryn , Riana 2,5
10 Kathryn , Janina 2,6
11
Julia , Sofia 3,4
12
13 Julia , Riana 3,5
14 Julia , Janina 3,6
15 Sofia , Riana 4,5
Sofia , Janina 4,6
Riana , Janina 5,6
YEARS IN THE
EMPLOYEES
BUSINESS (x)
Liza 1
Kathryn 2
Julia 3
Sofia 4
Riana 5
Janina 6
STEP 3. OBSERVATION EMPLOYEES YEARS
1 1,2 1.5
1 Liza , Kathryn 1.5
2
2 2
2
Liza , Julia 1,3
3 2.5
3 Liza , Sofia 1,4 2.5
4 3
4 1,5 3
5 Liza , Riana 3.5
5 1,6 3.5
6 Liza , Janina 2.5
6
7 Kathryn , Julia 2,3 2.5
3
7
8 Kathryn , Sofia 2,4 3
3.5
9
8 2,5 4
3.5
Kathryn , Riana
10
9 2,6 3.5
4
Kathryn , Janina
11 4
10
10 Julia , Sofia 3,4 3.5
3.5
12 4.5
11
11 Julia , Riana 3,5 4
4
13 4.5
12 Julia , Janina 3,6 4.5
14 5
13
13
15 Sofia , Riana 4,5 4.5
4.5
5.5
14
14 4,6
TOTAL 5
52.5
5
Sofia , Janina
15
15 Riana , Janina 5,6 5.5
5.5
TOTAL
TOTAL 52.5
52.5
•
2
𝞢(´𝑥 −𝜇 ´𝑥 ) 17.50
√ √
𝜎 ´𝑥 =
NCn
=
15
=√ 1.17=𝟏.𝟎𝟖
𝜇= 𝜇 ´
𝑥