Class 5 - inference_overview

# Class 5 - inference_overview - Measurement type Population...

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Categorical Proportion (Qualitative) SE(p^) Numerical Mean (Quantitative) SE(y-bar) Variance Measurement type Population or Phenomenon Characteristic (Parameter) Sample Characteristic, Point Estimate (Statistic) Variation associated with the location estimator Standard Error of the Estimate SE(statistic) calculated for a sample of n denoted by p or p^ Measures the location of the distribution center denoted by µ or y-bar Measures the variation or spread of the distribution denoted by σ 2 s 2 The Proportion & Mean are both location parameters. The variance measures spread, hence it is not a location parameter and no Standard Error is determined. y p ˆ

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CV = Critical Value = z* Confidence Interval for a location parameter Estimate ± Margin of Error Hypothesis for a location parameter ME = (Critical Value) SE SE = Standard Error p^ ± (CV) SE(p^) H 0 : p = p 0 H A : p (< or or >) p 0 H 0 : μ = μ 0 H A : μ (< or or >) μ 0 y-bar ± (CV) SE(y-bar) (Estimate) - (Null hypothesis value) TS = -------------------------------------------- SE(Estimate) ) ˆ ( ˆ 0 p SE p p TS - = ) ( 0 y SE y TS μ - = n s t y n ± - 1
Theoretical Standard Error of p^ [note that the Sharpe text uses q in place of (1-p) ] Sharpe Text calls this the Standard Deviation of p^ (note that Standard Error is a standard deviation of a statistic) Sharpe Text calls this a Standard Deviation of p^ & uses the notation SD(p Sample based estimate of Standard Error of p^ using p^ to estimate p This Standard Error is used to calculate Confidence Intervals Hypothesis based estimate of Standard Error of p^ for H 0 p = p 0 This Standard Error is used to test H 0 : p = p 0 n p p p SE ) 1 ( ) ˆ ( - = n p p p SE ) ˆ 1 ( ˆ ) ( - = n p p p SE ) 1 ( ) ˆ ( 0 0 - =

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p^)
Theoretical Standard Error of y-bar (note that Standard Error is a standard deviation of a statistic) Sharpe Text calls this the Standard Deviation of y-bar

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