ch09 - 9-1 Hypothesis Testing9-1.1 Statistical

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Unformatted text preview: 9-1 Hypothesis Testing9-1.1 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.9-1 Hypothesis Testing9-1.1 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. 9-1 Hypothesis Testing9-1.1 Statistical Hypothesesnull hypothesisalternative hypothesisOne-sided Alternative HypothesesTwo-sided Alternative Hypothesis9-1 Hypothesis Testing9-1.1 Statistical HypothesesTest of a Hypothesis• A procedure leading to a decision about a particular hypothesis• Hypothesis-testing 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.9-1 Hypothesis Testing9-1.2 Tests of Statistical HypothesesFigure 9-1Decision criteria for testing H:μ= 50 centimeters per second versus H1:μ ≠50 centimeters per second.9-1 Hypothesis Testing9-1.2 Tests of Statistical HypothesesDefinitions9-1 Hypothesis Testing9-1.2 Tests of Statistical HypothesesSometimes the type I error probability is called the significance level, or the α-error, or the sizeof the test.9-1 Hypothesis Testing9-1.2 Tests of Statistical Hypotheses9-1 Hypothesis Testing9-1 Hypothesis TestingFigure 9-3The probability of type II error when μ= 52 and n= 10.9-1 Hypothesis Testing9-1 Hypothesis TestingFigure 9-4The probability of type II error when μ= 50.5 and n= 10.9-1 Hypothesis Testing9-1 Hypothesis TestingFigure 9-5The probability of type II error when μ= 2 and n= 16.9-1 Hypothesis Testing9-1 Hypothesis Testing9-1 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.

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ch09 - 9-1 Hypothesis Testing9-1.1 Statistical

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