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Unformatted text preview: Hypothesis Testing Fundamentals by Harvey A. Singer I. Some Hypothesis Testing Terminology Statistical hypothesis: An assertion or conjecture about a parameter, or parameters, of the population. Null hypothesis ( H ) : A hypothesis that is maintained to be true until sufficient evidence to the contrary is obtained. Alternative hypothesis ( H 1 or H a ): A hypothesis against which the null hypothesis is tested and which will be held true if the null is found to be false. Simple hypothesis : A hypothesis that specifies a single value for a population parameter. Composite hypothesis : A hypothesis that specifies a range of values for a population parameter. One-sided alternative : An alternative hypothesis involving all possible values of a population parameter on either one side or the other (that is, greater than or less than) of the value specified in a simple null hypothesis. Two-sided alternative : An alternative hypothesis involving all possible values of a population parameter other than the value specified in a simple null hypothesis. Hypothesis test decisions : A decision rule (or rejection rule, or acceptance rule) is formulated under which the null hypothesis is accepted or rejected (in favor of the alternative hypothesis) on the basis of the sample evidence. Type I error : Reject a true null hypothesis. Type II error : Accept a false null hypothesis. Significance level : The probability of committing a type I error, that is, the probability of rejecting a true null hypothesis. Denoted by , and referred to as the x 100% significance level. Hence, Prob (type I error) = Prob (reject H | H true) = . The probability 1 of accepting a true null hypothesis is the confidence level. The confidence 1999 by Harvey A. Singer 1 level represents the probability of concluding that the specified value of the parameter being tested under the null hypothesis may be plausible....
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This note was uploaded on 01/26/2011 for the course OM 210 taught by Professor Singer during the Fall '08 term at George Mason.
- Fall '08