R g0 is unknown data n independent draws of

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Unformatted text preview: Example II: Coverage probability of mean in a response model when the standard deviation is unknown, and the distribution is Gaussian Model: Y = µ + R, .....R ~ G(0,σ ) , σ is UNKNOWN Data: n independent draws of r.vs Y1, Y2, € …Yn Observations: y1,y2,…yn Result: ~ T= µ− µ ~ σ n −1 ~ t n −1 n € Proof: See notes from class Algorithm: Step 1: From the t ­table, Find c such that P( ­c< tn ­1<c) =0.95 Step 2: The coverage interval is ( ~ ~ σ n −1 ~ σ n −1 µ− c , µ+ c ) n n ~ € Step 3: The confidence interval is ? Other results derived from the proof (i) The reason for sample s.d being divided by n ­1 (ii) Confidence interval for σ2. Definition: Pivotal Quantity Case III: Confidence interval for a Binomial model Case IV: Confidence interval for a regression model...
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This note was uploaded on 09/27/2012 for the course STAT 231 taught by Professor Cantremember during the Winter '08 term at Waterloo.

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