STATISTICAL INFERENCE

(Estimation)

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.

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.

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.

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.

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.

EX.

A firm wish to estimate amount of time its

salesman spend on each sales call.

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.

Confidence limit is

X ± z c (S.E.)

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

FINITE POPULATION

S.E. = σ ( N-n)

√ n (N-1)

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.

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 a95

percent confidence interval for the mean breaking

Strength of the population.6151 and 6249.

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.