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Unformatted text preview: 3/23/2009 1 91 Hypothesis Testing 91.1 Statistical Hypotheses Statistical 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 Definition experiment, in which the engineer is interested, for example, in comparing the mean of a population to a specified value. 91 Hypothesis Testing 91.1 Statistical Hypotheses 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. 91 Hypothesis Testing 91.1 Statistical Hypotheses null hypothesis alternative hypothesis Twosided Alternative Hypothesis Onesided Alternative Hypotheses 3/23/2009 2 91 Hypothesis Testing 91.1 Statistical Hypotheses Test 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 will conclude that the hypothesis is true ; if this information is inconsistent with the hypothesis, we will conclude that the hypothesis is false . 91 Hypothesis Testing 91.2 Tests of Statistical Hypotheses Figure 91 Decision criteria for testing H : = 50 centimeters per second versus H 1 : 50 centimeters per second. 91 Hypothesis Testing 91.2 Tests of Statistical Hypotheses Definitions 91 Hypothesis Testing 91.2 Tests of Statistical Hypotheses Sometimes the type I error probability is called the significance level , or the error , or the size of the test. 91 Hypothesis Testing 91.2 Tests of Statistical Hypotheses 91 Hypothesis Testing 3/23/2009 3 91 Hypothesis Testing Figure 93 The probability of type II error when = 52 and n = 10. 91 Hypothesis Testing 91 Hypothesis Testing Figure 94 The probability of type II error when = 50.5 and n = 10. 91 Hypothesis Testing 91 Hypothesis Testing Figure 95 The probability of type II error when = 2 and n = 16. 91 Hypothesis Testing 3/23/2009 4 91 Hypothesis Testing 91 Hypothesis Testing Definition The power is computed as 1  and power can be interpreted as The power is computed as 1 , and power can be interpreted as the probability of correctly rejecting a false null hypothesis....
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This note was uploaded on 02/05/2012 for the course ST 315 taught by Professor Staff during the Fall '11 term at S. Alabama.
 Fall '11
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