Hypothesis Testing
- Page ID
- 64218
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Hypothesis Testing
Hypothesis Testing \( \mu > 3 \) or Suppose that we want to test the hypothesis that \(\mu \ne 5 \). Then we can think of our opponent suggesting that \(\mu = 5 \). We call the opponent's hypothesis the null hypothesis and write: H0: \(\mu = 5 \) and our hypothesis the alternative hypothesis and write H1: \(\mu \ne 5 \) For the null hypothesis we always use equality, since we are comparing \( \mu \) with a previously determined mean. For the alternative hypothesis, we have the choices: < , > , or \( \ne \).
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 H0: \(\mu\) = .08 H1: \(\mu\) < .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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