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Published byEric Stanley Modified over 9 years ago
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Inference Concepts Confidence Regions
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Inference ConceptsSlide #2 Confidence Regions What is the next logical question when H 0 is rejected?
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95% Confidence Interval Concept Confidence IntervalsSlide #3 se se 95% of the samples provide a mean within what range?
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Confidence IntervalsSlide #4 se se Determine if is contained in the constructed 95% CI Mark x + 2SE -- this is a 95% CI Assume a sample results in the mean shown below YES
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Confidence IntervalsSlide #5 se se Repeat for more samples Sample #1 Sample #2 Sample #3 Sample #4 YES NO
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Confidence IntervalsSlide #6 se se So, how often will be contained in x + 2SE? What must happen for to be contained in the x+ 2SE interval? YES NO
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Confidence IntervalsSlide #7 The technique provides a range that contains 95% of the time. 95% Confidence Interval Concept
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Confidence IntervalsSlide #8 So, conclude that we are 95% confident* that is contained in this CI. *95% of all 95% CIs will contain . 95% Confidence Interval Concept
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Confidence IntervalsSlide #9 Not All CIs are 95% CIs, But the Concept Remains the Same The level of confidence used is 100(1- )% Look at ciSim() C=0.90C=0.95C=0.99 n % ContnM.E. % ContnM.E. % ContnM.E. 10 905.2956.2998.1 30 903.0953.6994.7 60 902.1952.5993.3
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Confidence IntervalsSlide #10 Constructing Any Confidence Region “Statistic” “sign” “margin-of-error” “Statistic” “sign” “constant” * SE ”statistic” General Specific
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What is Z* Comes from a Z~N(0,1) The Z that has the level of confidence “in the direction” of the H A –Exact constant depends on direction of H A Inference ConceptsSlide #11
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Inference ConceptsSlide #12 Confidence Regions if H A “not equals”, then ±Z* contains the level of confidence (C) interval likely contains the parameter if H A “less than”, then +Z* has C below upper bound for the parameter (parameter likely less) if H A “greater than”, then -Z* has C above lower bound for the parameter (parameter likely greater) C +z* C -z* C +z*-z*
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Inference ConceptsSlide #13 Confidence Regions Suppose that x=20, SE=3.5, and … –H A : < , =0.05 95% confident that is less than 25.76 –H A : ≠ , =0.05 95% confident that is between 13.14 & 26.86 –H A : > , =0.01 99% confident that is greater than 11.86 C +z* C -z* C
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