notes-10-25 - M4056 Hypothesis Testing. October 25, 2010 In...

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Unformatted text preview: M4056 Hypothesis Testing. October 25, 2010 In statistics, a hypothesis is a statement about a population parameter. Any hypothesis about a parameter , is equivalent to a statement of the form , where is a subset of the set of all possible values of . Hypothesis testing refers to the study rules for accepting or rejecting hypotheses, based on information from a sample. Obviously, rules can be made at whim unless we take into account the consequences of accepting or rejecting them. In due time, we will turn to these, but first we establish some vocabulary. Examples of hypotheses. 1. This coin is fair, i.e., a given Bernoulli variable X has parameter p = 1 / 2. 2. More than 40% of the registered voters in Baton Rouge are Republicans, i.e., the Bernoulli variable X , defined to be 1 if a randomly chosen voter in Baton Rouge is Republican and 0 otherwise, has parameter p . 4. 3. The mean weight of adult cats is between 9 and 11 pounds, i.e., the approximately normal random variable...
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