Stats 309 11-1a

# Stats 309 11-1a - 11.1 Hypothesis Testing In hypothesis...

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11.1 Hypothesis Testing In hypothesis testing, there is a preconceived idea about the value of the population parameter. For example, the dean of a business school claims that the average weekly salary of his graduates is \$800. Based on the evidence we saw, we suspect that the actual mean is lower than that. Thus, there are two theories or hypotheses involved in a statistical study: The first is what we assume to be true until we prove otherwise, called the null hypothesis , μ = 800, denoted H 0 . The second is the research or alternative hypothesis , μ < 800, denoted H a . The alternative hypothesis is what we are trying to prove is true. Next, we present our evidence. This is called the test statistic . This is our ‘evidence’ to see if we can back up our alternative hypothesis. That is what the sample statistic does. Then we set up a rejection region . The rejection region helps us make our final decision, so that everyone comes to the same decision. The final decision is our conclusion . In hypothesis testing, there are only two possible conclusions we can make:

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- We can reject the null hypothesis in favor of the alternative hypothesis. This is equivalent to the jury coming to the conclusion that the defendant is guilty. -Or, we can fail to reject the null hypothesis. This means we don’t have enough evidence to reject the null hypothesis and we don’t have enough evidence to accept the alternative hypothesis. The jury did not have enough evidence to convict. We never accept the null hypothesis! That would be the equivalent to the prosecutor saying the defendant is innocent. If the prosecutor thought the defendant was innocent, he wouldn’t be prosecuting him! He just didn’t have enough evidence to prove the guy was guilty. There are two possible errors that can be made here:
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## This note was uploaded on 04/06/2008 for the course MTHSC 309 taught by Professor Cathydavis during the Spring '08 term at Clemson.

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Stats 309 11-1a - 11.1 Hypothesis Testing In hypothesis...

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