Hypothesis Testing
Hypothesis Testing m > 3 or m 5. Suppose that we want to test the hypothesis that m 5. Then we can think of our opponent suggesting that m = 5. We call the opponent's hypothesis the null hypothesis and write: H_{0}: m = 5 and our hypothesis the alternative hypothesis and write H_{1}: m 5 For the null hypothesis we always use equality, since we are comparing m with a previously determined mean. For the alternative hypothesis, we have the choices: < , > , or .
Procedures in Hypothesis Testing When we test a hypothesis we proceed as follows:
Errors in Hypothesis Tests We define a type I error as the event of rejecting the null hypothesis when the null hypothesis was true. The probability of a type I error (a) is called the significance level. We define a type II error (with probability b) as the event of failing to reject the null hypothesis when the null hypothesis was false.
Example Suppose that you are a lawyer that is trying to establish that a company has been unfair to minorities with regard to salary increases. Suppose the mean salary increase per year is 8%. You set the null hypothesis to be H_{0}: m = .08 H_{1}: m < .08
Q. What is a type I error? A. We put sanctions on the company, when they were not being discriminatory.
Q. What is a type II error? A. We allow the company to go about its discriminatory ways. Note: Larger a results in a smaller b, and smaller a results in a larger b.
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