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Unformatted text preview: Covered Topics 81 Introduction • In the previous chapter we illustrated how a parameter can be estimated from sample data. However, it is important to understand how good is the estimate obtained. • Bounds that represent an interval of plausible values for a parameter are an example of an interval estimate . 82.1 Development of the Confidence Interval and its Basic Properties 82 Confidence Interval on the Mean of a Normal Distribution, Variance Known 82.1 Development of the Confidence Interval and its Basic Properties 82 Confidence Interval on the Mean of a Normal Distribution, Variance Known ¡ A confidence interval estimate for μ is an interval of the form l ≤ μ ≤ u, where the end points l and u are computed from the sample data. ¡ Because different samples will produce different values of l and u, these values are random variables. ¡ Suppose that we can determine values of L and U such that the following probability statement is true; P(L ≤ μ ≤ U) = 1 α 82 Confidence Interval on the Mean of a Normal Distribution, Variance Known ¡ Where ≤ α ≤ 1. ¡ There is a probability of 1 α of selecting a sample for which the confidence interval (CI) will contain the true value of μ . /2 U L μ 1 α /2 82 Confidence Interval on the Mean of a Normal Distribution, Variance Known ¡ The endpoints or bounds l and u are called lower and upper confidence limits , respectively. ¡ Since Z follows a standard normal distribution, we can write: Simplify: Definition 82 Confidence Interval on the Mean of a Normal Distribution, Variance Known Example 81 82 Confidence Interval on the Mean of a Normal Distribution, Variance Known ¡ Ten measurement of impact energy (J): 64.1, 64.7, 64.5., 64.6, 64.3, 64.5, 64.6, 64.8, 64.2, and 64.3 ¡ Assume that impact energy is normally distributed with σ =1 J....
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This note was uploaded on 10/12/2011 for the course STATISTICS 101 taught by Professor Nazim during the Spring '10 term at Qatar University.
 Spring '10
 nazim
 Probability

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