POPULATION: Population is an aggregate of objaects enimate or inenimate understudy. The population may be finite or infinite. SAMPLE: A finite subset of statistical individuals in a populations is called a sample and the number of individuals in a sample is called sample size.

NOTE: For the purpose of determining population characterstics instead of enumerating entire population the individuals in the sample only are observed.then the sample characterstics are utilized to approximately determine or estimate the population.

PARAMETERS: In order to avoid verbal confusion with the statistical constants of the population like mean, variance etc. of the population are known as parameters. Statistics: Statistical measure computed from the sample observation alone like mean, variance, mode etc. of sample have been termed as statistics.

SAMPLING DISTRIBUTION : The no. of possible samples of size ‘n’ that can be drawn from the finite population of size ‘N’ Is k = ( N! /n! * (N-n)!) For each of these ‘k’ samples we can compute some statistics ‘t’ Where ‘t’ = t( x1,x2,x3…………,xn )

Sample no. ‘t’ mean s 2 1 t ₁ barx ₁ Sq(s ₁ ) 2 t ₂ barx ₂ Sq(s ₂ ) 3 t ₃ barx ₃ Sq(s ₃ ) k tk barxkSq(sk) TABLE :

STANDARD ERROR: The standard deviation of the sampling distribution of a statistics is known as its standard error. The standard error of some of the well known statistic are given in the table. Where ‘n ’ is sample size, ‘ σ 2’ is the population variance, p is the population purportion.

Sr.no. statistics Standard error 1 Sample mean xbar σ /√n 2 Observed sample proportions ‘p’ √PQ/n 3 Sample s.d ‘s’ √ σ ₂ /2n 4 Sample variance Sq(s) σ ₂ /2n

5Sample quartile’Q’ σ / ѵ n 6Sample median’M’ σ / ѵ n 7Sample correlation coeff. ‘r’ (1- ρ 2)/ Ѵ n 8 Sample moment: μ ₃ σ 3 Ѵ 96/n 9 Sample moment: μ ₄ σ 4 Ѵ 96/n 10Sample coeff. Of variation’v’ v/ Ѵ 2n

UTILITY OF STANDARD ERROR S.E play a very important role in the large sample theory and forms the basis of the testing of hypothesis. If ‘t’ is any statistics, then for large sample Z= (t-E(t)) / Ѵ V(t) ~ N(0,1 )

Thus if the discrepancy between the observed and expected values of the statistics is greter than ‘ 1.96 time’ the standard error. The hypothesis is rejected at 5% level of significance (L.O.S)

Principle steps of sample survey: 1.Objects of the survey 2.Defining the population to the sample. 3.The frame and sampling unit. 4.Data to be collected. 5.Method of collected information..

6.Interview method. 7.Mailed questionnaire method. 8.Non respondent. 9.The frame and sampling unit. 10. Data to be collected

The principle of sample survey The theory of sampling is based on the following important principles. Principle of statistical regularity. Principle of validity. Principle of optimization.

ERROR: The errors involved in the collection of processing and Analysis of a data may be broadly classified under the following two heads:  SAMPLING ERRORS  NON-SAMPLING ERRORS

SAMPLING ERRORS: Sampling errors have their origin in sampling and arise due to the fact that only a part of the population i.e sample has been used to estimate population parameters and draw inference about the population. As such the sampling errors are absent in a complete enumeration survey.

Sampling biases are primarily due to the following reasons:  SUBSTITUTION  FAULTY DEMARCATION OF SAMPLING UNITS  FAULTY SELECTION OF SAMPLES

Eg. If x1,x2,x3……………xn is a sample of independent obervations then the sample variance s²=∑(xi-barx)²/n As an estimate of the population variance σ ² is biased where as the statistics ∑(xi-barx)²/n-1 Is an unbiased estimate of σ ²

Non –sampling error: Non sampling error can occur at every stage of the planning or execution of census or sample survey. The preparation of an exhaustive list of all the saurces of non sampling errors is a very difficult task. However a care ful examination of the major faces of a survey indicates that some of the more important non sampling errors arise from the following factors :

 Faulty planning or definitions  Response errors  Failure of respondent memory  Non response biases  Compiling errors  Publication errors Main factors

ADVANTAGE OF SAMPLE SURVEY  less time : - There is considerable saving in time and labor since only a part of the population has to be examined. The sampling results can be obtained more rapidly and data can be analyzed much faster.  REDUCED COST OF THE SURVEY : -sampling usually results in reduction in cost in term of money and in term of man hours. Although the amount of labor and the expenses involved in collecting information are generally greater per unit of sample then in complete enumeration, the total cost of the sample survey is expected to be much smaller than that oif the complete census.

 Greater accuracy of results: The results of a sample survey are usually much more reliable than those obtained from complete census due to the following reason :

1) it is always possible to determine the extent of the sampling error. 2) The non sampling error due to factors such as training of field workers, measuring and recording observations, location of unit etc. are likely to be of serious nature in complete census than in a sample sample survey

 Important: In a sample survey non- sampling errors can be controlled more effectively by employing more qualified and better trained personnel.

 Greater scope: Sample survey has generally greater scope as compared with the complete census. The complete enumeration is impracticable.

EXAMPLES TREES IN A JUNGLE, WE ARE LEFT WITH NO WAY BUT TO RESORT TO SAMPLING. TESTING THE QUALITY OF MILK.

TESTING THE BREAKING STRENGTH OF CHALKS. TESTING THE LIFE OF AN ELECTRIC BULB OR TUBE ETC.

 Complete enumeration is impracticable and sampling technique is the only method to be used in such cases

LIMITATIONS OF SAMPLING

 Inspite of the fact that a proper choice of design is employed a sample does not fully cover the parent population and consequently results are not exact.

 sampling theory and its applications in the field need the survey of trained and qualified persons.

 The Planning and Execution of sample survey should be done very carefully or the data may provide misleading results.

TYPES OF SAMPLE SURVEY  DESCRIPTIVE SAMPLE SURVEY  ANALYTICAL SAMPLE SURVEY

SOME BASIC QUESTIONS FROM SAMPLING PROCESS ARE:  How should the observations should be made.  How many observations should be made.  How should the total?

ASSIGNMENT

What is population. Define sample with suitable eg.. Define sampling distribution. Define standard error. define principle steps of sample survey in detail. define limitations of sample survey.

1. What are the principle steps of sample survey? Discuss in detail? 2. Explain utility of standard error? 3. Define Simple Random Sampling without replacement? 4. In Simple random sampling prove that sample mean is an unbiased estimate of population mean?