Page 380 - DMTH404_STATISTICS

Statistics Richa Nandra, Lovely Professional University

Notes Unit 27: T - Distributions

CONTENTS

Objectives
Introduction
27.1 The Student's T-Distribution
27.2 T test

27.3 Summary
27.4 Keywords
27.4 Self Assessment
27.5 Review Questions

27.6 Further Readings

Objectives

After studying this unit, you will be able to:

 Discuss T - Distribution
 Explain example of T - Distribution

Introduction

In last unit you have studied about chi-square. This unit will provide you information related to
T - Distribution.
27.1 The Student's T-Distribution

Let X , X ...... X be n independent random variables from a normal population with mean m and
1 2 n
standard deviation s (unknown).
æ 1 2 ö
When s is not known, it is estimated by s, the sample standard deviation s = å ( X - X ) ÷ .
ç
i
è n 1- ø
-
X m
In such a case we would like to know the exact distribution of the statistic and the answer
s/ n
to this is provided by t - distribution.

X m
-
W.S. Gosset defined t statistic as t = which follows t - distribution with (n - 1) degrees of
s/ n
freedom.

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