Lec16 - IOE/Stat IOE/Stat 265, Fall 2009 Lecture #16:...

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IOE/Stat 265, Fall 2009 Lecture #16: ectu e 6 Statistical Intervals (for Averages) Based on a Single Sample as d o a S g Sa p 7.1 Basic Properties of Confidence Intervals 7.2 Larger Sample Intervals for Means and Proportions 7.3 Intervals Based on Normal Population 7.4 Confidence Intervals for Variance (and Std Dev) r Normal Populations 1 for Normal Populations Types of Interval Estimates 3 Types of Interval Estimates nfidence interval ounds population and ± A confidence interval bounds population and distribution parameters (such and μ, σ, π ) ± A tolerance interval bounds a selected proportion of a distribution ± A prediction interval bounds future observations from the population or distribution. 2 hat is a Confidence Interval? What is a Confidence Interval? ± A Confidence Interval (CI) identifies 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. ± Chances of being wrong, α (a decision variable) ± Most Common α = 0.05 then 95% CI ± 95% represents the confidence level that the CI will apture the true parameter value capture the true parameter value ± Note: the higher the confidence level required, the wider the CI 3 actors Influencing CI Factors Influencing CI ample size n ± Sample size, n ± Variance of process, σ 2 ,and rror risk lso known as the Type I Error) ± Error risk, α (also known as the Type I Error) which represents the probability that the interval does not contain the true value of the parameter 4
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ecall Lec 13 lide 33) Recall Lec.13 (Slide 33) y the Central Limit Theorem (pg 215 18) ± By the Central Limit Theorem (pg 215-218) μ x Z~ N ( 0 , 1 ) −μ = σ n ± Solve for μ 5 7-2 Normal Mean Confidence Interval (Variance known or n large >30) or mean from a normal population with ± For mean, μ , from a normal population with known σ , I Lower I Upper Z X σ μ α + 2 / 2 / CI Lower CI Upper n 1 −α 6 α /2 α /2 xample 1: C I Influencing Factors Example 1: C.I. Influencing Factors ± Suppose you calculate a sample mean = 1 mm based on 5 samples. (assume known
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This note was uploaded on 03/17/2010 for the course IOE 265 taught by Professor Garyherrin during the Fall '09 term at University of Michigan-Dearborn.

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Lec16 - IOE/Stat IOE/Stat 265, Fall 2009 Lecture #16:...

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