Hypothesis Testing of Single Mean and Single Proportion: Rare Events
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Hypothesis Testing of Single Mean and Single Proportion: Rare Events
1.8
2008/06/06 17:33:19 GMT-5
2012/06/14 04:37:06.822 GMT-5
Barbara
Illowsky
Barbara Illowsky, Ph.D.
illowskybarbara@deanza.edu
Maxfield Foundation
Maxfield Foundation
cnx@cnx.org
Susan
Dean
Susan Dean
deansusan@deanza.edu
Connexions
Connexions
cnx@cnx.org
sdean billowsky
sdean billowsky cnxorg
MaxfieldFoundation
elementary
statistics
Mathematics and Statistics
en
Suppose you make an assumption about a property of the population (this assumption
is the null hypothesis). Then you gather sample data randomly. If the sample has
properties that would be very unlikely to occur if the assumption is true, then you
would conclude that your assumption about the population is probably incorrect.
(Remember that your assumption is just an assumption - it is not a fact and it may or
may not be true. But your sample data are real and the data are showing you a fact that seems to
contradict your assumption.)For example, Didi and Ali are at a birthday party of a very wealthy friend. They hurry
to be first in line to grab a prize from a tall basket that they cannot see inside because
they will be blindfolded. There are 200 plastic bubbles in the basket and Didi and Ali
have been told that there is only one with a $100 bill. Didi is the first person to reach
into the basket and pull out a bubble. Her bubble contains a $100 bill. The
probability of this happening is 1200=0.005. Because this is so unlikely, Ali is hoping
that what the two of them were told is wrong and there are more $100 bills in the
basket. A "rare event" has occurred (Didi getting the $100 bill) so Ali doubts the
assumption about only one $100 bill being in the basket.
Hypothesis
A statement about the value of a population parameter. In case of two hypotheses, the statement assumed to be true is called the null hypothesis (notation
H0 size 12{H rSub { size 8{0} } } {}) and the contradictory statement is called the alternate hypothesis (notation
Ha size 12{H rSub { size 8{a} } } {}).