This preview shows page 1. Sign up to view the full content.
Unformatted text preview: f the Chebychev inequality states that the probability that a random variable
1
diﬀers from its mean by a or more standard deviations is less than or equal to a2 .
Conﬁdence Intervals The Chebychev inequality can be used to provide conﬁdence intervals on
estimators. Conﬁdence intervals are often given when some percentages are estimated based on
samples from a large population. For example, an opinion poll report might state that, based on
a survey of some voters, 64% favor a certain proposal, with polling accuracy ±5%. In this case,
we would call [59%, 69%] the conﬁdence interval. Also, although it is not always made explicit,
there is usually a level of conﬁdence associated with the conﬁdence interval. For example, a 95%
conﬁdence in a conﬁdence interval means the probability the true percentage is in the interval is at
least 95%.
In practice, the true fraction of voters that favor a certain proposition might be a given number,
say p. In order to estimate p we could selec...
View
Full
Document
This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.
 Spring '08
 Zahrn
 The Land

Click to edit the document details