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#### 2.3.1.2 Definitions

Definition 15   Given a Model for a set of observations, a Hypothesis Test (HT) involves:
1. The null hypothesis . This is the hypothesis under which we will evaluate the data. is a statement about the distribution underlying the data.
2. The alternative hypothesis . This is an alternative statement about the data distribution. The goal of a hypothesis test is to choose between and .
3. The test statistic . This is a function of the data (a random variable) with the following two properties:
• Under we know something about the distribution of .
• is relevant to the choice vs.
4. The critical region . A set of values that are used to reject the null hypothesis. In other words, the null hypothesis is rejected whenever the value we observe for is in .

In the toxic fish example we have:

• Model: 25 i.i.d. trials. At each trial we select a fish from the lake and test if it is toxic or not.
• :
• :
• : # number of toxic fish in our 25 fish sample.
• : .

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Eran Borenstein
2007-05-04