1. STATISTICAL INFERENCE
(Estimation)

2. 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.
Statistical inference may be of two kinds: parameter estimation
and Hypothesis testing.

3. 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.

4. 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.

5. COMPARISON BETWEEN ESTIMATION AND
HYPOTHESIS TESTING
• Utilises 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.

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.

7. EX.
A firm wish to estimate amount of time its
salesman spend on each sales call.

8. 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.

9. Confidence limit is
X ± z c (S.E.)

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

11. FINITE POPULATION
S.E. = σ ( N-n)
√ n (N-1)

12. EX 1
From a random sample of 36 New Delhi civil
service personnel, the mean age and the
sample
standard deviation were found to be 40 years
and 4.5 years respectively. Construct a 95 per
cent confidence interval for the mean age of
civil
servants in New delhi.
40 ±1.47 years.

13. EX2
The quality department of a wire manufacturing
company periodically selects a sample of wire
specimens in order to test for breaking strength.
Past experience has shown that the breaking
strength of a certain type of wire are normally
distributed with standard deviation of 200 kg. A
random sample of 64 specimens gave a mean of
6,200 kg. The quality control supervisor wanted a
95
percent confidence interval for the mean breaking
Strength of the population.6151 and 6249.

14. EX 3
A manager wants an estimate of average sales of salesman
in his company. A random sample of 100 out of 500
salesmen is selected and average sales is found to be
Rs. 750( thousand). Given population standard deviation is
Rs. 150 (thousand) , manager specifies a 98% confidence
interval. What is the interval estimate for average sales of
salesman?
718720 to 781280.