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Week2AMTB2304

# Week2AMTB2304 - Dr Suren Phansalker ADM2304 MiniTab...

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Dr. Suren Phansalker ADM2304 MiniTab Approach to Confidence Intervals & Hypothesis Tests For Single Population Mean Some Basic Theory: (This is Strictly Optional!) When σ = σ (X) is known, {This is not the usual case} ( ) ~ ( ) , ( ) X X N E X X n σ μ σ = = / 2 / 2 1 ( ) X P z z X α α μ α σ < < = / 2 / 2 ( 1){ } ( 1) ( 1) 1 ( ) X P z z X α α μ α σ > > − = / 2 / 2 1 ( ) X P z z X α α μ α σ > > − = ( ) / 2 / 2 ( ) ( ) 1 P X z X X z X α α σ μ σ + > > = α , or ( ) / 2 / 2 ( ) ( ) 1 P X z X X z X α α σ μ σ < < + = α This is the CI: / 2 / 2 ( ) ( ) X z X X z α α σ μ σ < < + X This is some times written as: CI: / 2 / 2 ( ) ( ) X X z X X z n α α σ σ ± = ± When σ = σ (X) is not known and must be estimated by calculating, s = s(X) 1 ( ) ~ ( ) , ( ) n s X s X t E X s X n n μ = = = {This is the usual case} / 2 / 2 ( 1) ( 1) 1 ( ) X P t n t n s X α α μ α < < = / 2 / 2 ( 1){ } ( 1) ( 1) ( 1) ( 1) 1 ( ) X P t n t n s X α α μ α > > − = / 2 / 2 ( 1) ( 1) 1 ( ) X P t n t n s X α α μ α > > − = ( ) / 2 / 2 ( 1) ( ) ( 1) ( ) 1 P X t n s X X t n s X α α μ α + > > = , or ( ) / 2 / 2 ( 1) ( ) ( 1) ( ) 1 P X t n s X X t n s X α α μ α < < + = This is the CI: / 2 / 2 ( 1) ( ) ( 1) ( ) X t n s X X t n s X α α μ < < + , some times also written as CI: / 2 / 2 / 2 ( ) ( 1) ( ) ( 1) ( 1) s X s X t n s X X t n X t n n n α α α ± = ± = ± 1

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