Hypothesis_testing

# Hypothesis_testing - Hypothesis Testing Author John M...

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Hypothesis Testing Author: John M. Cimbala, Penn State University Latest revision: 13 February 2007 Introduction An important part of statistics is hypothesis testing making a decision about some hypothesis (reject or accept), based on statistical methods . The four basic steps in any kind of hypothesis testing are: o Determine the null hypothesis and the alternative hypothesis . o Collect data and determine a test statistic . o Determine how unlikely the test statistic would be if the null hypothesis were true . o Make a decision based on the test statistic. These steps will become clearer when we do some example problems. Hypotheses First, we need to clarify the difference between a null hypothesis and an alternative hypothesis : o A null hypothesis is defined as a theory that is being considered or tested . The null hypothesis has not been proven by a test, and may or may not be true. In many cases, the null hypothesis represents “nothing is happening,” hence the adjective “null.” o An alternative hypothesis , also called a research hypothesis , is defined as the complement of the null hypothesis . The alternative hypothesis is typically the opposite of the null hypothesis, and is the theory that the researchers are trying to prove (or disprove). A common application is in testing the relationship between two variables , as in clinical studies of drugs or lifestyles. Here are some examples: o Is there a statistically significant relationship between taking one aspirin each day and the risk of heart attack? ± Null hypothesis : There is no relationship between taking one aspirin each day and the risk of heart attack. ± Alternative hypothesis : There is a relationship between taking one aspirin each day and the risk of heart attack. o Is there a statistically significant relationship between drinking one can of beer before driving, and having a car accident? ± Null hypothesis : There is no relationship between drinking one can of beer before driving, and having a car accident. ± Alternative hypothesis : There is a relationship between drinking one can of beer before driving, and having a car accident. The χ 2 distribution is typically used for relationship studies, and the test statistic is called a chi-square statistic . Another common application is to test hypotheses about the population mean of a variable . In these types of problems, there are two parts to the null hypothesis: o The critical value of a variable under consideration (we set the null hypothesis to this value). o The type and side of the tail(s) of concern in the hypothesis test: ± Two-tailed test : We are concerned about values less than or greater than the critical value. ± Left-tailed test : We are concerned about values less than the critical value.

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## This note was uploaded on 07/23/2008 for the course ME 345 taught by Professor Staff during the Spring '08 term at Penn State.

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Hypothesis_testing - Hypothesis Testing Author John M...

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