The rejection region is the range of values that, under a specified confidence level, it is impossible for the null hypothesis to be a valid answser. Using the z-score from the given data, you find the level of possibility (the p value) for a given value at H-zero, and if that p is less than the threshold specified in the problem (usually as α=0.05), then H-zero is rejected.If p is greater than that line, then there is a possibility that H-zero can be possible, not proven true, but accepted as a possibility.Statisticians find this kind of hypothesis testing as a key part of the scientific method. If a hypothesis can be proven false in the math on the drawing board, it can save a lot of money in the testing stage.
There was a classic case in California of a blonde woman with a ponytail and a black man with a beard and moustache who drove a yellow car who were arrested and convicted after a mugging. Prosecutors used the facts that these two were near, and their features that matched the description made it a surety that they were the ones who committed the crime. They used probabilities that a the car was yellow was 1 in 10, that the man had a beard was 1 in 4, and that she had a ponytail was 1 in 10, and so on to prove that the chances that it was not them to be more than 12 million to one, so since there are not 12 million people in San Pedro, these must be the ones. Under appeal, the board stated that "In any event, we think that under the circumstances the "trial by mathematics" so distorted the role of the jury and so disadvantaged counsel for the defense, as to constitute in itself a miscarriage of justice," and overturned the verdict.
There is an old saying that if you cannot dazzle them with dexterity, baffle them with baloney. Both the jurors and the defense attorney were baffled.
Ohh, here is a better link for an article about the case: http://www.maa.org/devlin/devlin_07_08_07.html
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