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CHAPTER 8 : SAMPLING THEORY

8.1 Population

Any well defined set (group) of objects about which a statistical enquiry is being made is called a population or universe.

The total number of objects (individuals or members) in a population is known as the size of the population which may be finite or infinite.

The population can refer to things as well as people.

For example,

  • All members of the cultural society of your city.

  • All students of mathematics of Ithaca college.

  • All Americans who saw 'TITANIC' last year.

  • Heights of all students of your school.

  • Weights of all the citizens of city of New York above 20 years of age.

  • Mileages of automobiles tyres of Dunlop. etc.

A population is finite if it contains finite numbers of individuals. For example, the ages of 20 boys of your class.

A population is infinite if it contains infinite number of individuals. For example, the pressures at various points in the atmosphere.


Often, statisticians want to know things about population, but they fail to do so almost because in every case such data for every individual of the population is not available. Suppose I am a researcher in the field of 'Tuberculosis' (TB). I want to learn how many Indians suffer from it. It would not be practical (or perhaps even impossible) to contact every Indian. Thus whenever we want to study the characteristic of a certain population, it is difficult to study the whole population. it is often expensive and time consuming and many times we lack resources for the study of the whole population. In any science we cannot study more than a part of population. A part or small section selected from the population is called a sample.

Index

8.1 Population
8.2 Sample
8.3 Parameters and Statistic
8.4 Sampling Distribution
8.5 Sampling Error
8.6 Central Limit Theorem
8.7 Critical Region
8.8 Testing of Hypothesis
8.9 Errors in Tesitng of Hypothesis
8.10 Power o a Hypothesis Test
8.11 Sampling of Variables
8.12 Sampling of Attributes
8.13 Estimation
8.14 Testing the Difference Between Means
8.15 Test for Difference Between Proportions
8.16 Two Tailed and one Tailed Tests
8.17 Test of Significance for Small Samples
8.18 Students t-distribution
8.19 Distribution of 't' for Comparison of Two Samples Means Independent Samples
8.20 Testing Difference Between Mens of Two Samples Dependent Samples or Matched Paired Observations
8.21 Chi-Square
8.22 Sampling Theory of Correlation
8.23 Sampling Theory of Regression

Chapter 1





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