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ch9 - 9-1 Hypothesis Testing 9 1H th i T ti 9-1.1...

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H th i T ti 9-1 Hypothesis Testing 9-1.1 Statistical Hypotheses Statistical hypothesis testing and confidence interval timation of parameters are the fundamental methods estimation of parameters are the fundamental methods used at the data analysis stage of a comparative xperiment which the engineer is interested for experiment, in which the engineer is interested, for example, in comparing the mean of a population to a ecified value efinition specified value. Definition
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H th i T ti 9-1 Hypothesis Testing 9-1.1 Statistical Hypotheses For example, suppose that we are interested in the urning rate of a solid propellant used to power aircrew 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 te (a parameter of this distribution) rate (a parameter of this distribution). • Specifically, we are interested in deciding whether or not the mean burning rate is 50 centimeters per second.
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H th i T ti 9-1 Hypothesis Testing 9-1.1 Statistical Hypotheses Two-sided Alternative Hypothesis null hypothesis alternative hypothesis One-sided Alternative Hypotheses yp
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9-1 Hypothesis Testing 9-1.1 Statistical Hypotheses Test 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 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 .
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9-1 Hypothesis Testing 9-1.2 Tests of Statistical Hypotheses Figure 9-1 Decision criteria for testing H : μ = 50 centimeters per g g 0 p second versus H 1 : μ≠ 50 centimeters per second.
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9-1 Hypothesis Testing 9-1.2 Tests of Statistical Hypotheses Definitions
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9-1 Hypothesis Testing 9-1.2 Tests of Statistical Hypotheses Sometimes the type I error probability is called the ignificance level r the rror r the ze f the test significance level , or the α -error , or the size of the test.
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9-1 Hypothesis Testing 9-1.2 Tests of Statistical Hypotheses
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9-1 Hypothesis Testing
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9-1 Hypothesis Testing Figure 9-3 The probability of type II error when μ = 52 and n = 10.
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9-1 Hypothesis Testing
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9-1 Hypothesis Testing Figure 9-4 The probability of type II error when μ = 50.5 and n = 10.
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9-1 Hypothesis Testing Figure 9-5 The probability of type II error when μ = 2 and n = 16.
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9-1 Hypothesis Testing
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9-1 Hypothesis Testing Definition he power is computed as 1 - and power can be interpreted as 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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ch9 - 9-1 Hypothesis Testing 9 1H th i T ti 9-1.1...

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