# Lecture 10 - Change in Homework 2 Assigned Problems:...

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Change in Homework 2 Assigned Problems: Chapter 8 problems will now be due with HW Assignment 3 on April 4, 2008. HW Assignment 2 due on March 4, 2008 will include only Chapter 5 and 7 problems. Exam 2 will be limited to Chapters 5 and 7.

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Problem 7-7 (page 262) Impact of sample size on interval width
7-7 n Z x σ α 2 ± a.) To halve the width, increase n by a factor of 2 2 or 4 b.) Increasing n by a factor of 25 decreases width by a factor of 5 (2 5 5 ) =

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Problem 7-11 (page 263) Interpretation of CI’s, approx. to binomial
1000 95% CI’s How many capture the true mean value? (“correctness” is a Bernoulli process) 7-11 ( ) () ( ) 0.95 : 1000 1 940 960 :~ , 1 939.5 960.5 Ex n p p Binomial n V x np p Px NormalApprox X N np np p σ = = = =− ≤≤

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() 5 . 1 5 . 1 5 . 1 892 . 6 950 5 . 960 5 . 1 892 . 6 950 5 . 939 + + = = Z P x x σ μ
Regardless of the input distribution, if the sample size n is sufficiently large, the standardized variable: Z = (Xbar- μ )/(s/ n) has an approximately normal distribution . This implies that: Xbar ± Z α /2 s/ n is a large-sample confidence interval for μ with confidence level approximating 100(1- α )%.

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Problem 7-12 (page 268) Large sample confidence intervals
7-12 110 0.81sec 0.34 nx s == = Large Sample . 0.0324 0.01 s Std Error n α = 58 . 2 005 . 0 Z 58 . 2 005 . 0 2 Z Z = [] 2 0.726,0.894 s xZ n ±⇒

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Confidence Intervals on a Proportion The unbiased estimator of the proportion of successes in a random sample of n Bernoulli trials is x/n, where x is the number of observed successes in a sample. If n is large, p’=x/n follows an approximately Normal distribution with EV=p and VAR=p(1-p)/n . It follows that standardizing p’ implies that: P(-Z α /2 < (p’-p)/( p(1-p)/n) < +Z α /2 ) 1- α
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## This note was uploaded on 04/08/2008 for the course ENGR 2600 taught by Professor Malmborg during the Spring '08 term at Rensselaer Polytechnic Institute.

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Lecture 10 - Change in Homework 2 Assigned Problems:...

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