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Unformatted text preview: 1 Statistical Inference • The field of statistical inference consists of those methods used to make decisions or draw conclusions about a population . • These methods utilize the information contained in a sample from the population in drawing conclusions. 1 Statistical Inference2 Point Estimation2 Point Estimation2 Point Estimation3 Hypothesis Testing We like to think of statistical hypothesis testing as 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 (e.g. mean pull strength). 43.1 Statistical Hypotheses3 Hypothesis Testing For 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 mean burning rate (a parameter of this distribution). • Specifically, we are interested in deciding whether or not the mean burning rate is 50 centimeters per second. 43.1 Statistical Hypotheses3 Hypothesis Testing 43.1 Statistical Hypotheses Twosided Alternative Hypothesis Onesided Alternative Hypotheses3 Hypothesis Testing 43.1 Statistical Hypotheses est 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 consistent with the hypothesis, then we ill conclude that the hypothesis is true ; if this information is inconsistent with the hypothesis, we will conclude that the hypothesis is false .3 Hypothesis Testing 43.2 Testing Statistical Hypotheses3 Hypothesis Testing 43.2 Testing Statistical Hypotheses3 Hypothesis Testing 43.2 Testing Statistical Hypotheses Sometimes the type I error probability is called the significance level , or the αerror , or the size of the test.3 Hypothesis Testing 43.2 Testing Statistical Hypotheses3 Hypothesis Testing 43.2 Testing Statistical Hypotheses3 Hypothesis Testing 43.2 Testing Statistical Hypotheses3 Hypothesis Testing 43.2 Testing Statistical Hypotheses3 Hypothesis Testing 43.2 Testing Statistical Hypotheses3 Hypothesis Testing 43.2 Testing Statistical Hypotheses • The power is computed as 1  β , and power can be interpreted as the probability of correctly rejecting a false null hypothesis ....
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This note was uploaded on 12/25/2010 for the course ALL 0204 taught by Professor 79979 during the Spring '10 term at National Chiao Tung University.
 Spring '10
 79979

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