ch09_Class Notes till 11.16.09_1

# ch09_Class Notes till 11.16.09_1 - 9-1 Hypothesis Testing...

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9-1 Hypothesis Testing 9-1.1 Statistical Hypotheses Definition 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 example, in comparing the mean of a population to a specified value.
9-1 Hypothesis Testing 9-1.1 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.

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9-1 Hypothesis Testing 9-1.1 Statistical Hypotheses null hypothesis alternative hypothesis One-sided Alternative Hypotheses Two-sided Alternative Hypothesis
Hypotheses are always statements about the population or distribution under study, not statements about the sample. The value of the population parameter specified in the null hypothesis (50 centimeters per second in the above example) is usually determined from past experience or knowledge of the process, or even from previous tests or experiments from some theory or model regarding the process under study from external considerations, such as design or engineering specifications, or from contractual obligations.

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A procedure leading to a decision about a particular hypothesis is called a test of a hypothesis. A hypothesis-testing procedure should be developed with the probability of reaching a wrong conclusion in mind. The null hypothesis will always be stated so that it specifies an exact value of the parameter (as in the statement H 0 : μ = 50 centimeters per second)
Exercise 9.1 In each of the following situations, state whether it is a correctly stated hypothesis testing problem and why. Yes, because the hypothesis is stated in terms of the parameter of interest, inequality is in the alternative hypothesis, and the value in the null and alternative hypotheses matches.

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Exercise 9.1 - Continued In each of the following situations, state whether it is a correctly stated hypothesis testing problem and why. No, because the inequality is in the null hypothesis.
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• Fall '10
• Ferekides
• Electrical Engineering, Null hypothesis, Statistical hypothesis testing, 9-1 Hypothesis Testing

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