100(1-alpha) Confidence Interval for μ when μ and σ^2 are unknown

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Homework Help Overview

The discussion revolves around finding a 100(1-alpha) confidence interval for the mean μ when both μ and σ² are unknown, utilizing a random sample from a normal distribution.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the use of estimators for μ and question the clarity of the original problem statement. There is mention of using the t-distribution as a potential approach.

Discussion Status

The discussion is ongoing, with some participants seeking clarification on the problem and others suggesting methods to approach the confidence interval calculation. No consensus has been reached yet.

Contextual Notes

There appears to be confusion regarding the formulation of the question and the appropriate statistical methods to apply, particularly concerning the use of the t-distribution.

cimmerian
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Homework Statement



X1,...Xn is a random sample from N(μ, σ^2)

Homework Equations



Estimator of μ maybe?

a1 + a2 = a
a1 = a2 = a/2

(x-μ)/(σ/√n)~N(0,1)

((x-μ)/σ)^2~Chi square(1)

The Attempt at a Solution



I tried to replace μ with its estimator xbar but that gives me 0.
 
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This may just be me, but I don't see the question in this.
 
I'm supposed to find the 100(1 - alpha) confidence interval for μ
 
cimmerian said:
I'm supposed to find the 100(1 - alpha) confidence interval for μ

Then use the t-distribution; that is what it was made for.

RGV
 

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