ENMATH 4
ENGINEERING DATA ANALYSIS
Sampling distributions and
point of estimation
Reporter: Nicole Gamase
Ma. Victoria Espiritu
BSABE-3B
SAMPLING AND DISTRIBUTION AND POINT
OF ESTIMATION
Sampling Distribution
A sampling distribution is a probability
distribution of a statistic obtained from a
larger number of samples drawn from a
specific population. The sampling distribution
of a given population is the distribution of
frequencies of a range of different outcomes
that could possibly occur for a statistic of
a population.
EXAMPLE:
Instead of polling asking 1000
owners what cat food their per
prefers, you could repeat your
poll multiple times.
SUBTOPICS:
Point of Estimation
Sampling distribution and the
Central Theorem
General concept of point
estimation
POINT ESTIMATION
POINT ESTIMATE
An estimate of a population parameter given by
a single number is called estimate.
POINT ESTIMATOR
A point estimator is a statistic for estimating the
population parameter e and will be denoted by
e*
POINT AND INTERVAL ESTIMATION:
Point estimation
When a single value is used as an estimate, the estimate is called a
point estimate of population parameter.
Interval estimation
Generally, there are situations where point estimation is not
desirable and we are interested in finding limits with in which the
parameter would be expected to lie is called an interval estimation.
CONFIDENCE INTERVAL
EXAMPLE:
PROPERTIES OF POINT ESTIMATORS
 1. BIAS -The bias of a point estimator is defined as the
difference between the expected value of the estimator
and the value of the parameter being estimated.
 2. CONSISTENCY -Tells us how close the point
estimator stays to the value of the parameter as it
increases in size.
 3. MOST EFFICIENT OR UNBIASED -The most efficient
point estimator is the one with the smallest variance of
all the unbiased and consistent estimators.
SAMPLING DISTRIBUTION OF THE SAMPLE MEAN
Inferential testing uses the sample mean (x) to estimate the
population mean (µ). Typically, we use the data from a single
sample, but there are many possible samples of the same size
that could be drawn from that population.
the distribution of the sample mean will have a mean equal to µ.
it will have a standard deviation (standard error) equal to σ/√n
EXAMPLE:
THE CENTRAL LIMIT THEOREM
It states that the sampling distribution of the
sample means will approach a normal distribution as
the sample size increases.
There are 3 different components of the central
limit theorem:
µ= is the population
σ= is the population standard deviation
n= is the sample size
TO CALCULATE THE CLT
EXAMPLE:
 The age that American females first have intercourse is
on average 17.4 years, with a standard deviation of
approximately 2 years ("The Kinsey institute," 2013).
This random variable is not normally distributed, though
it is somewhat mound shaped.
a. State the random variable.
b. Suppose a sample of 35 American females is taken.
Find the probability that the mean age that these 35
females first had intercourse is more than 21 years.
SOLUTION:
SAMPLING DISTRIBUTION OF THE
SAMPLE PROPORTION
The population proportion (p) is a parameter that is as
commonly estimated as the mean. It is just as important
to understand the distribution of the sample proportion,
as the mean. The sample proportion is calculated by:
where x is the number of elements in your population
with the characteristic and n is the sample size
SAMPLING DISTRIBUTION OF THE SAMPLE PORTION
EXAMPLE:
EXAMPLE:
Suppose that in a population of voters in a certain region
38% are in favor of particular bond issue. Nine hundred
randomly selected voters are asked if they favor the bond
issue.
1.Verify that the sample proportion p^ computed from
samples of size 900 meets the condition that its sampling
distribution be approximately normal.
2.Find the probability that the sample proportion computed
from a sample of size 900 will be within 5 percentage
points of the true population proportion.
SOLUTION:
GENERAL CONCEPT OF POINT
ESTIMATION
Point estimation, in statistics, the process of finding an approximate
value of some parameter such as the average of a population from
random samples of the population.
A point estimate of a parameter θ is a value that is a sensible guess
for θ
 A point estimate is obtained by a formula (“estimator”) which takes
the sample data and produces an point estimate.
Formulas are called point estimators of θ.
Different samples produce different estimates, even though you use
the same estimator.
Thank you for listening!!