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
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
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
- The Land