# Lec17 - IOE/Stat IOE/Stat 265, Fall 2009 Lecture #17:...

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IOE/Stat 265, Fall 2009 Lecture #17: ectu e Statistical Intervals (for Variances and Proportions) Based on a Single Sample opo o s) 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 ddendum to Lec 16 Addendum to Lec 16 ± Student “t” Distribution v1 2 2 1x 2 + ⎛⎞ ⎜⎟ ⎝⎠ + ⎡⎤ Γ ⎢⎥ f(x )1 v v v 2 ⎣⎦ =+ π Γ E(x) 0 v V(x) for v>2 = = () v 2 skew = 0 2 6 kurtosis for v>4 v4 = ttp://en wikipedia org/wiki/Image:Student densite best JPG http://en.wikipedia.org/wiki/Image:Student_densite_best.JPG 3 xcel Functions Excel Functions DIST(x v tails) omplementary Cumulative of ± TDIST(x, v, tails) ± Returns the Student’s t-distribution Co p e e ta y Cu u at e o ± TINV ( α , v) ± Returns inverse of Student’s t-distribution ± Assumes two-sided (e.g. α /2 each tail) ± Appx A-5 (pg. 671) ± Provides inverse of Student’s t-distribution ssumes one- ded 4 ± Assumes one sided

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xample 1: Example 1: Assume X follows a “t” Distribution with v=10 “degrees of freedom”: ± Prob (X > 1.812) = ± Prob (X < -1.372) = TDIST(1.372,10,1)=0.10 ± Prob (X > 2.5)= ind s ch that P ob (X > ) 05 5 ± Find x such that Prob (X > x) = .05 hi quared ( Distribution Chi-Squared ( χ 2 ) Distribution ± Let ν be a positive integer. ± The rv X is Chi-Squared with parameter, ν , if the pdf of X is the gamma density function with α = ν /2 and β =2. (/ 2 )1 x / 2 1 e x 0 ν−− /2 xe f(x; ) 2( / 2 ) 0o t h e r w i s e ν ν= Γν ± Using Minitab, generate Chi-Squared Distributions for
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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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Lec17 - IOE/Stat IOE/Stat 265, Fall 2009 Lecture #17:...

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