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In any hypothesis-testing problem, because we take action based on incomplete information, there is a built-in danger of an erroneous decision. A statistical test procedure based on sample data will lead to precisely one of the following four situations. Two of these situations will entail correct decisions and the other two, incorrect decisions.
* fro is true and is accepted a correct decision.
* Ho is true and Ho is rejected—an incorrect decision.
* Ho is false and Ho is accepted—an incorrect decision.
* Ho is false and Ho is rejected—a correct decision.
Rejection of the null hypothesis when in fact it is true is called a Type I error or a rejection error. The probability of committing this error is denoted by the Greek letter a (alpha) and is referred to as the level of significance of the test.
Acceptance of H0 when it is false is called a Type II error or an acceptance error. The Replica IWC probability of making this error is denoted by the Greek letter (3(beta). Ideally, we would like to have both a and 3 very low. In fact, if it were possible, we would eliminate both these errors and set their probabilities equal to zero. However, once the sample size is agreed upon, there is no way to exercise simultaneous control over both errors. The only way to accomplish this simultaneous reduction is to increase the sample size, and if we want both a and 3 equal to zero,cartier love bracelet white gold sale, to explore the entire population.
To understand the basic approach to hypothesis testing, we might recall the familiar presumption under our judicial system. "The accused is innocent until proven guilty beyond a reasonable doubt." Is the accused guilty? That is the question. We state the null hypothesis as H0: The accused is not guilty. The alternative hypothesis is HA: The accused is guilty.
It is up to the prosecution to provide evidence to destroy the null hypothesis. If the prosecution is unable to provide such evidence, the accused goes free. If the null hypothesis is refuted, we accept the alternative hypothesis and declare that the accused is guilty. Bear in mind that if the accused goes free, it does not mean that the accused is indeed innocent. It simply means that there was not enough evidence to find the accused guilty. Nor, if the accused is cotwicted, does it mean that the accused did indeed commit the crime. It simply means that the evidence vase so overwhelming that it is highly improbable that the accused is innocent. Only the accused knows the truth.
In this context, suppose the accused is innocent, in fact, but is found guilty. Then a Type I error has been made because the null hypothesis has been rejected erroneously. Thus, the probability of convicting the innocent would be a, and we would like to keep this value rather low. On the other hand, if a guilty person is declared not guilty, a Type II error has been made with probability,
In approaching the problem of testing a statistical hypothesis, our attitude will be to Cartier Replica Watches assume initially that the null hypothesis Ho is correct. It will be up to the experimental data to provide evidence, beyond reasonable doubt, that will refute this notion. We will then reject Ho and opt for HA. Otherwise, the status quo prevails in that we have no reason to believe otherwise. The evidence from the experimental data should be extremely strong for us to go along with the hypothesis HA. When we reject the null hypothesis, we have not proved that it is false,cartier love ring yellow gold price, for no statistical test can give 100 percent assurance of anything. However, if we reject Ho with a small a, then we are able to assert that Ho is false and HA is true beyond a reasonable doubt. Thus, in any test procedure, it makes good sense to let a be small.
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