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ioe265f11-Lec16 - Lec16 Confidence Intervals for Mean and...

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Lec16 - Confidence Intervals for Mean and Proportion IOE 265 - Fall 2011 1 1 Statistical Confidence Intervals: Mean and Proportion 2 Topics I. What is a Confidence Interval (CI)? II. 100(1- )% Confidence Interval III. Sample Size and Confidence IV. Confidence Intervals Population mean, proportion, p
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Lec16 - Confidence Intervals for Mean and Proportion IOE 265 - Fall 2011 2 3 I. What is a Confidence Interval? Confidence Intervals (CI) identify a plausible range of values (CI lower ~ CI upper ) for a point estimate. Plausibility is defined by the probability the interval includes the true population parameter. Most Common = 0.05 OR 95% CI 95% represents the confidence level or a probability of 0.95 that the CI will trap the true parameter value Note: the higher the confidence level, the wider the CI 4 Factors Influencing CI Sample size Variance of the sample data, and Acceptance for error (also known as the level or error) - represents the probability that the interval does not trap the true value of the parameter
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Lec16 - Confidence Intervals for Mean and Proportion IOE 265 - Fall 2011 3 5 Sampling Distribution… By the Central Limit Theorem Solve for x Z ~ N(0,1) n   6 Example: C.I. Influencing Factors Suppose you calculate a sample mean = 1 mm based on 5 samples. (assume known = 0.17 and the data are normally distributed). Identify a 95% CI for the mean. What happens to the CI range if: is reduced to 0.01 (CI ?) n is increased to 10 samples (other variables remain same)? = 0.10
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Lec16 - Confidence Intervals for Mean and Proportion IOE 265 - Fall 2011 4 7 CI Interpretation (95% CI) In the long run, 95% of the intervals will
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