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Unformatted text preview: 91 Hypothesis Testing91.1 Statistical HypothesesDefinitionStatistical hypothesis testing and confidence interval estimation of parameters are the fundamental methods used at the data analysis stage of a comparative experiment, in which the engineer is interested, for example, in comparing the mean of a population to a specified value.91 Hypothesis Testing91.1 Statistical HypothesesFor example, suppose that we are interested in the burning rate of a solid propellant used to power aircrew escape systems. • Now burning rate is a random variable that can be described by a probability distribution. • Suppose that our interest focuses on the meanburning rate (a parameter of this distribution). • Specifically, we are interested in deciding whether or not the mean burning rate is 50 centimeters per second. 91 Hypothesis Testing91.1 Statistical Hypothesesnull hypothesisalternative hypothesisOnesided Alternative HypothesesTwosided Alternative Hypothesis91 Hypothesis Testing91.1 Statistical HypothesesTest of a Hypothesis• A procedure leading to a decision about a particular hypothesis• Hypothesistesting procedures rely on using the information in a random sample from the population of interest. • If this information is consistentwith the hypothesis, then we will conclude that the hypothesis is true; if this information is inconsistentwith the hypothesis, we will conclude that the hypothesis is false.91 Hypothesis Testing91.2 Tests of Statistical HypothesesFigure 91Decision criteria for testing H:μ= 50 centimeters per second versus H1:μ ≠50 centimeters per second.91 Hypothesis Testing91.2 Tests of Statistical HypothesesDefinitions91 Hypothesis Testing91.2 Tests of Statistical HypothesesSometimes the type I error probability is called the significance level, or the αerror, or the sizeof the test.91 Hypothesis Testing91.2 Tests of Statistical Hypotheses91 Hypothesis Testing91 Hypothesis TestingFigure 93The probability of type II error when μ= 52 and n= 10.91 Hypothesis Testing91 Hypothesis TestingFigure 94The probability of type II error when μ= 50.5 and n= 10.91 Hypothesis Testing91 Hypothesis TestingFigure 95The probability of type II error when μ= 2 and n= 16.91 Hypothesis Testing91 Hypothesis Testing91 Hypothesis TestingDefinition• The power is computed as 1 β, and power can be interpreted as the probability of correctly rejecting a false null hypothesis. We often compare statistical tests by comparing their power properties....
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This note was uploaded on 09/21/2010 for the course EIN 3235 taught by Professor Zhai during the Spring '10 term at FIU.
 Spring '10
 Zhai

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