Page 360 - DMTH404_STATISTICS

Statistics Richa Nandra, Lovely Professional University

Notes Unit 25: Chi - Sqaure ( ) Distribution
2

CONTENTS

Objectives
Introduction
25.1 Chi - Square Distribution
25.1.1 Sampling Distribution of Variance

25.2 Summary
25.3 Keywords
25.4 Self Assessment
25.5 Review Questions

25.6 Further Readings

Objectives

After studying this unit, you will be able to:
2
 Discuss Chi - Square ( ) Distribution
 Describe some examples related to Chi - Square

Introduction

When sampling is done with replacement, each unit of the population has a probability of its
1
selection equal to . Further, there are N possible samples that are equally likely, and therefore,
n
N 1
the probability of selection of each sample is n .
N
When sampling is done without replacement, the units are either drawn one by one, without
replacement, or all the n units are selected in one attempt. We know that the permutations of N
N
objects taking n at a time is P and this becomes the number of ordered samples. Corresponding
n
1
N
to this, the number of unordered samples will be C , each with probability N . In this case
n C n
1
also, the probability of selection of a unit at any draw is . For example, the probability of
N
1
selection of a unit at the first draw = , the probability of its selection at the second draw is
N
N - 1 1 1
× = and so on, the probability of its selection at the rth draw is
N N - 1 N
-
-
+
-
N 1 N 2 N r 1 1 1
× ×  × =
N N 1 N r 2 N r 1 N
- +
-
- +
352 LOVELY PROFESSIONAL UNIVERSITY