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Lecture 9

Lecture 9 - Confidence Intervals.pdf

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Department
Mathematics
Course
MAT2377
Professor
Aziz Khanchi
Semester
Fall

Description
MAT23773XSpring2011IntervalEstimationSections81to83and85RecallTheobservedvalueofanestimatorforanunknownparameterx35theniscalledapointestimateForexampleifthesamplemeanisthelatterisapointestimateforthepopulationmeanRemarkThepointestimatetellsusnothingabouttheaccuracyofthexofOnewaytoanswerthequestionestimateThatishowcloseisofaccuracyistoconstructanintervalofvaluessuchthatwewillbehighlycondentthatwillbeinthisintervalGeneralIdeaforCondenceIntervalsSupposethatissomeunbknownparameterandthatweareusingthestatistichXXas1nanestimatorforSupposefurthermorethatwecanndtwostatisticsLLXXandUUXX1n1nbusuallybaseduponsuchthat1PLUwhereisaconstantbetween0and1Usually1willbealargevalueeg9095or99LetlandubetheobservedvaluesofLandUrespectivelyWesaythatluisa1001condenceintervalforTerminology11iscalledthecondencelevelorcondencecoecient2iscalledtheerrorrate3ullengthoftheintervalisameasureoftheprecisionoftheestimateAsmallerlengthintervalisinterpretedasamorepreciseestimation1
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