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Interval Estimation for Non-Normal Distributions: Derivation of Confidence Interval, Study notes of Statistics

The derivation of the confidence interval for estimating the mean of a non-normal distribution using the interval estimator. It covers the concept of interval estimation, the role of coverage probability, and the use of random samples. The document also discusses the two-stage approximation method when the sample size is large and when the variance is unknown.

What you will learn

  • What is the role of coverage probability in interval estimation?
  • What is interval estimation and how is it used to estimate the mean of a non-normal distribution?

Typology: Study notes

2020/2021

Uploaded on 03/13/2021

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chapter 8

Internal Estimation

D Interval Estimator

The random (^) interval ( L (^) , U ) (^) forms an^ interval estimator^ of O U - L B (^) the width (^) of interval coverage probability PC^

L (^ Xi,^ '^

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6T T

rt d

O Normalwithunknom#

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6 with unbiased estimator S =

) #^ E.^ Hi^

- E

) ' looll-HY.anfidenceihterralfvtf-X-tE.mx

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Find neck^ , aka such^ that ki - - X't- E. n-i

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where X n^ x'n - i

k (^) - =

WE, n - I

< : p (^ Kc MT < ka (^) ) =^ (^ TT -^ 6- < (^) ft ) =^ I^

  • L ""I÷÷÷;ma t::I÷¥i÷÷ . )