Lecture 10

# Lecture 10 - Probability and Statistics in the Life...

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Probability and Statistics in the Life Sciences (Spring 2010) AMS 110.02 Lecture 10 (chap7) Donghyung Lee

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Chapter 7 (supplements) Hypothesis Testing Hypothesis Testing In chapter 6, we discussed methods of interval estimation for parameter of various distributions. Researchers often have preconceived ideas about what these parameters might be and wish to test whether the data confirm with these ideas. This type of question is formulated in a hypothesis- testing framework by specifying a null and alternative hypothesis. Hypothesis testing is the process by which we draw some conclusion about a population parameter using information contained in a sample of observations. Hypothesis tests are always done under the assumption that the null hypothesis is true . They ask a question, “Is it likely that I would have observed my test statistic if the null hypothesis were true?” If it is likely, then we do not reject the null hypothesis and if it is unlikely, then we reject the null hypothesis.
Chapter 7 (supplements) Hypothesis Testing Definition 7.1 A hypothesis is a statement of a theory or a claim. Definition 7.2 - A null hypothesis (or tested hypothesis), denoted by , is a statistical hypothesis the truth of which is to be tested by sampling. - In general, the null hypothesis represents what one would believe. Definition 7.3 - A alternative hypothesis ( ) is a competing hypothesis to the null hypothesis. - In general, the alternative hypothesis is a statement that the researcher is trying to establish. 0 H 1 a H or H

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Chapter 7 (supplements) Hypothesis Testing Definition 7.4 (from other textbook) The null hypothesis , denoted by , is the claim about one or more population characteristics that is initially assumed to be true (the “prior belief” claim). The
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## Lecture 10 - Probability and Statistics in the Life...

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