STATISTIC AND PROBABILITY-Week-5.DWLPppt

Another information on statistics and probability

1. STATISTICS and
PROBABILITY
Sampling and
Sampling
Distributions

2. Session Objectives
At the end of the session, the participants
will be able to
1.illustrate random sampling
2.distinguish between parameter and
statistic
3.identify sampling distributions of statistics
(sample mean)

3. Sampling
Distributions
Standard
Error of the
Sampling
Distribution of
the Sample
Proportion
Mean of the
Sampling
Distribution of
the Sample
Proportion
The Central
Limit Theorem
Variance and
Standard
Deviation of the
Sampling
Distribution of
the Sample
Mean
Mean of the
Sampling
Distribution of
the Sample
Mean
Sampling Distribution of
the Sample Proportion
Sampling Distribution
of the Sample Mean

4. Four Types of Random Sampling
1.Simple Random Sampling is a sampling
technique in which every element of the population
has the same probability of being selected for
inclusion in the sample.
2.Systematic Random Sampling is a sampling
technique in which every kth element of the
population is selected until the desired number of
elements in the sample is obtained. The value of k
is calculated by dividing the number of elements in
the population by the number of elements in the
desired sample. The value of k is the sampling
interval.

5. 3. Stratified Random Sampling is a sampling
technique in which the population is first divided
into strata and then samples are randomly
selected separately from each stratum.
4. Cluster or Area Sampling is a random
sampling technique in which the entire
population in broken into small groups, or
clusters, and then, some of the clusters are
randomly selected. The data from the randomly
selected clusters are the ones that are
analyzed.

6. Exercises: Identify the type of sampling
technique used by the researcher in each
situation:
1.The office clerk gave the researcher a list of
500 Grade 10 students. The researcher
selected every 20
th
name on the list.
2. A researcher selected a sample of n = 120
from a population of 850 by using the Table of
Random Numbers.
Systematic Random Sampling
Simple Random Sampling

7. 3. A statistician selected a sample of n =
100 high school students from a private
school with 2,500 students. He randomly
selected the students from each year level.
4. A researcher randomly selected 5
barangays from 10 barangays in a town.
Stratified Random Sampling
Cluster Random Sampling

9. Sampling Distribution of Sample Means

10. Example :
Consider the population consisting of
the values 2, 3, and 5. List all the
possible samples of size 2 that can be
drawn from the population with
replacement. Then, compute the mean
x for each sample. Lastly, find the
mean of the sampling distribution of
means and the mean of the population.