learn about stat

1. STATISTICAL INFERENCE
By: Syed Abdul Basit

2. Definition
The main objective of sampling is to draw
conclusions about the unknown population from the
information provided by a sample. This is called
statistical inference.

3. Kinds Of Statistical Inference
parameter estimation
Hypothesis testing

4. PARAMETER ESTIMATION
Parameter estimation is concerned with
obtaining numerical values of the parameter
from a sample.
Example, a company may be interested in
estimating the share of the population who are
aware of its product

5. Estimation process
Estimation (or estimating) is the process of
finding an estimate, or approximation, which is
a value that is usable for some purpose even if
input data may be incomplete, uncertain, or
unstable.

6. POINT ESTIMATION AND INTERVAL
ESTIMATION
An estimate of the population parameter given
by a single number is called is called a point
estimate of the parameter
Example: A firm wish to estimate amount of
time its salesman spend on each sales call.

7. INTERVAL ESTIMATION
An estimate of a population parameter given
by two numbers between which the parameter
may be considered to lie. The interval
estimation consists of lower and upper limits
and we assign a probability (say 95%
confidence) that this interval contains the true
value of the parameter.

8. Confidence limit
X ± z c (S.E.)

9. HYPOTHESIS TESTING
On the other hand, hypothesis is concerned
with passing a judgment on some assumption
which we make( on the basis of some theory
or information) about a true value of a
population parameter.

10. Types of hypothesis
Null hypothesis
Alternative hypothesis
Composite hypothesis
Simple hypothesis

11. Null hypothesis
Any hypothesis denoted by (Ho) which is to be
test for possible rejection under the
assumption that is true is called null
hypothesis
µ=µo

12. Alternative hypothesis
The hypothesis is accepted when the null
hypothesis has been rejected is called
alternative hypothesis. It is denoted by h1.
µ≠µo

13. COMPARISON BETWEEN ESTIMATION AND
HYPOTHESIS TESTING
 Utilizes the information of a sample .
 In parameter estimation we use some formula in which we
substitute the observations of a sample in order to obtain
numerical estimate of the population parameter.
 In hypothesis testing we begin with some assumption about
the true value of the population parameter.
 Then we calculate certain test statistic and draw conclusion.
POINT ESTIMATION AND INTERVAL ESTIMATION

14. STANDARD ERROR
Standard deviation of sample statistic is called
standard error. Infinite Population
 Standard error of mean when population S.D
(σ) is known. S.E. = σ /√ n
 Standard error of mean when population S.D
(σ) is not known. S.E. = s/ √ n