This document discusses statistical inference, which involves drawing conclusions about an unknown population based on a sample. There are two main types of statistical inference: parameter estimation and hypothesis testing. Parameter estimation involves obtaining numerical values of population parameters from a sample, like estimating the percentage of people aware of a product. Hypothesis testing involves making judgments about assumptions regarding population parameters based on sample data. The document also discusses point estimation, interval estimation, standard error, and provides examples of calculating confidence intervals.

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.