So... we make an error when we estimate

Transcription

1 8. Samplg Dstrbuto of the Mea Pg 6/Ex 7. A populato of 7 studets has ages The populato mea ( ) 0.7 Estmate the populato mea by takg a radom sample of studets 9 5 Fd the sample mea but 0.7 Error.96 So... we make a error whe we estmate the populato mea from a sample from that populato. MAT 0 Dr Jack Lubowsky Pg Small populato of studet grades. Populato mea ( ) 60. Sample studets, calc sample mea , error Sample studets, calc sample mea , error Sample 4 studets, calc sample mea , error MAT 0 Dr Jack Lubowsky Pg Calculate the mea ad stadard devato of a populato. Populato of People Populato of People Sample of People x Σ( - ) ( - ) Calculate the mea value of the sample MAT 0 Dr Jack Lubowsky Pg MAT 0 Dr Jack Lubowsky Pg 4

2 Σ( - ) Take a umber of samples of sze may samples of sze... people Make a dstrbuto of the sample meas. people people people 000??? MAT 0 Dr Jack Lubowsky Pg 5 MAT 0 Dr Jack Lubowsky Pg 6 Make a dstrbuto of the sample meas. OTICE: If the Populato s Make a dstrbuto ormal of the sample meas. the the Dstrbuto of Sample Meas s ormal MAT 0 Dr Jack Lubowsky Pg 7 MAT 0 Dr Jack Lubowsky Pg 8

3 If the Populato s ormal the Make the a dstrbuto of the sample meas. Dstrbuto of Sample Meas s ormal 000 MAT 0 Dr Jack Lubowsky Pg 9 o-ormal Dstrbutos of Populatos AOTHER OTICE: Cetral Lmt Theorem Regardless of the shape of the populato dstrbuto, the sample dstrbuto of the mea approaches a ormal Dstrbuto as the sample sze becomes large. ( Geerally > 0 ) Samplg Dstrbuto of the Mea for > 0 MAT 0 Dr Jack Lubowsky Pg 0 Samplg Dstrbuto of the Mea: Effect of Sample Sze Populato 60 0 Populato Sample Sze Sample Sze Sample Sze Sample Sze Take Samples k Dstrbuto of sample meas. x s the Stadard Error of the Mea MAT 0 Dr Jack Lubowsky Pg MAT 0 Dr Jack Lubowsky Pg

4 Smlar to Pg 47/Prob 9 The mea weght of ewbor babes a Log Islad commuty s 7.5 lbs. wth a stadard devato of.4 pouds. What s the probablty that. a baby wll wegh < 7. lbs?. a radom sample of 49 babes wll have a mea weght of < 7. lbs.? Dstrbuto of Weghts Populato Probablty that a baby wll be less tha 7. lbs ormalcdf (-E99, 7., 7.5,.4 ) The Lfe of a Car Battery A maufacturer of automoble batteres states that ther slow de battery has a mea lfe of 50 moths wth a stadard devato of 6 moths. If a cosumer protecto group radomly samples 49 of these batteres, what s the probablty that the mea lfetme of the cosumer group s sample wll be less tha 48 moths (assumg the maufacturers clam s true)? x 7. Probablty that a sample of 49 babes wll have a mea weght of less tha 7. lbs ormalcdf (-E99, 7., 7.5, 0. ) Dstrbuto of Sample Mea Weghts.4/ moths 6 moths Sample Sze 49 Lookg for Prob of sample meas < 48 moths MAT 0 Dr Jack Lubowsky Pg MAT 0 Dr Jack Lubowsky Pg 4 Probablty that a Sgle Battery wll last < 48 Moths Secto 7.7: Samplg Dstrbuto of the Proporto Probablty that a battery wll last less tha 48 moths ormalcdf -E99,48,50, Probablty that a group of 49 batteres wll last less tha 48 moths 48 Probablty that a Sample of 49 batteres wll have a Mea Lfetme < 48 moths ormalcdf -E99,48,50, A populato of people ca be composed of dfferet groups (e.g democrats, Brooklytes, college graduates, etc.). A populato of tems made by a maufacturer ca be composed of dfferet groups of tems (tems to sell at full prce, tems to sell at dscout, tems ot saleable.) A populato of tra arrval tmes ca be composed of dfferet categores ( Less tha mute late, more tha but less tha 5 mutes late, etc.) A proporto s the fracto equal to the umber of tems oe group dvded by the total umber of tems. MAT 0 Dr Jack Lubowsky Pg 5 MAT 0 Dr Jack Lubowsky Pg 6

5 Secto 8.7: Samplg Dstrbuto of the Proporto Proporto Fracto of the populato wth a characterstc p /... the true proporto occurreces the populato populato x / sample proporto x occurreces the sample sample sze The Samplg Dstrbuto of the Proporto ca be approxmated by a ormal Dstrbuto f... p > 5 ad (-p) > 5 Example of a Proporto Populato assau Commuty College ,000 Studets Females: 0,450 Populato Proporto / 0,450 / 9, Sample of 50 Studets from assau Commuty College 50 Females: x 9 p proporto of females ˆp estm of p p Sample x Estmate of Populato Proporto x/ 9 / Samplg Dstrbuto of the Proporto p ˆp ˆp p p( p) stadard error of the proporto MAT 0 Dr Jack Lubowsky Pg 7 p Stadard Error of the Proporto ˆp p( p) MAT 0 Dr Jack Lubowsky Pg 8 Cosder a Electo DD p.5 MM ( - p).47 Take a Sample of 50 voters. 50 What s the dstrbuto of sample proportos for samples of sze 50? Samplg Dstrbuto of the Proporto for DD ˆp p. 5 5 % p( p). 5(. 47) ˆp 50 ˆp % Problems: 8. The Samplg Dstrbuto of the Mea Page 409/0 8. The Mea ad Stadard Devato of the Samplg Dstrbuto of the Mea. Page 40/0 8.4 The Shape of the Samplg Dstrbuto of the Mea Page 4/4a, c, e, & g 8.5 Calculatg Probabltes Usg the Samplg Dstrbuto of the Mea Page 4/ 46, The Effect of Sample Sze o the Stadard Error of the Mea Page 4/5, 54, The Sample Dstrbuto of the Proporto Page 4/68,70, 7,76 Geeral Page 44/84, 86, 88, 5 MAT 0 Dr Jack Lubowsky Pg 9 MAT 0 Dr Jack Lubowsky Pg 0