Act 3.1 Random Rectangles PDF

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homework from module 3.1...

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Activity 3.1 – Random Rectangles Task 1 – Guessing the average area of all rectangles—Three Methods 1. Looka tt hes hee tf oraf e ws e c ondsandwr i t edo wnyourgues sa st ot hea ve r a gea r e aoft her e c t angl e sont hes hee t . Re membe rt ha tt hea v er a gear e as houl dbes ome whe r ebe t we e nt hes ma l l e s tr e c t a ngl e( 1uni tofa r e a)andt hel a r ge s t r e c t angl e( 1 8uni t sofa r e a) Gues sofAver a geAr ea: 8uni t s

2. Now s el e c tfiver e c t a ngl est hat ,i nyourj udgment ,a r er epr es ent a t i veoft her e c t a ngl e sont hi spa ge .Wr i t edownt he a r e af ore ac hoft hefive .Comput et hea ve r a geoft hefivear e as . Re c t angl e# 4 1 Ar e aofRe c t angl e 1 6

2 5 18

1 8 4

82 6

6 2 3

Ha nds e l e c t edSa mpl eAver ageAr e a:9. 4uni t s

3. Now us ear andom numbe rgene r a t ort os e l e c t5di s t i nc tr a ndom r e c t angl e sbe t we e n1and100 .The nfindt hea ve r a ge a r e aoft he s e5r ec t a ngl es . t ps : / /www. r a ndom. or g/i nt e ge r s / Got o:ht Ge ne r a t e5numbe rbet we en1and1 00ass hownbe l ow

The s ear et her ec t angl enumbe r s ,now gofindt her ec t angl ea r e as Re c t angl e#

55

38

17

8

16

Ar eaofRe c t a ngl e 16

9

9

1

1

2uni t s Ra ndom Sa mpl eAver a geAr ea :7.

Task 2 – Computing the Bias Theda t af r om apr e vi ouss e c t i onofSTAT1 10ha vebee npr ovi de di nt hefil er andom_ r ec t _s a mpl es _f al l _ 16. j mp 1. Us eJ MPt oc r ea t eas i de b ys i deboxpl o t s( wi t hl abe l e dmea nl i nes )oft hea ve r a gear eaf ort het hr e egue s s e st y pe s ( gue s s , s ub j e c t i v e ,r a ndo m) .Pa s t eas c r e ens hotbe l ow a nddes c r i bet heas s oc i at i on.

Sc r eens hot :

The bias of a statistic is the average amount that the statistic over or underestimates the parameter of interest.

2. Le t ’ sc omput et hedi ffe r enc ebet we e nt hepur eg ue s s e sa nda c t ua lva l ue .

´x pure guess =9.17 b. μactual =7.47 c . bia s pure guesses =´x pure guess−μ actual=+ 1.7

a .

Ona ve r a ge , how muc hdot hepur egue s s e sove r -orunde r e s t i ma t et heac t ualv al ue ? Th eb i a so ft h egue s s e swa s+1 . 7uni t so fa r e a ,i nd i c a t i ngt hegue s s e sove r e s t i mat e dt h ea r e ab y1. 7uni t s ,o na v e r a ge . 3. Re pe att hel a s tpr obl e m,butt hi st i mef ort hes ub j e c t i ves a mpl e s . a . b. c .

´x subjective=9.46 μactual =7.47 bia s subjective=´x subjective−μ actual =1.99

Ona ve r a ge , how muc hdot hepur egue s s e sove r -orunde r e s t i ma t et heac t ualv al ue ? Thebi asoft hegue s s e swas+1 . 9 9uni t sofa r e a , i ndi c at i ngt hegues s eso ve r e s t i mat edt hea r eaby1. 99uni t s ,on a ve r a ge . 4. Fi na l l y ,c ompl et et hec al c ul at i onsf ort her a ndo ms a mpl e s . a . ´x random=7.59

b. c .

μactual =7.47 ´x random −μactual =0.12

Ona ve r a ge , how muc hdot hepur egue s s e sove r -orunde r e s t i ma t et heac t ualv al ue ? Thebi asoft hegue s s e swas+0 . 1 2uni t sofa r e a , i ndi c at i ngt hegues s eso ve r e s t i mat edt hea r eaby0. 12uni t s ,on a ve r a ge .

Task 3 – Final Analysis A statistic is called unbiased if it has a bias of 0, i.e. it DOESN’T over or underestimate the parameter, on average. 5. Whi c hoft het hr e epr oc e dur e s( pur egues s i ng, mea nofas ubj e c t i v es ampl e ,orme anofar a ndom s a mpl e , l e adst o a n( appr ox i ma t e l y)unbi as eds t at i s t i c ? Iwoul ds a yt ha ta ppr oxi ma t e l yt heme anofar andom s a mpl el e adst oanunbi as e ds t a t i s t i cbe c aus et her a ndom s ampl ei sonl yoff+0 . 1 2uni t sofar e af r om t hepur egue s s es .

6. S t a t i s t i c i answhengi ve nac hoi c e ,s t a t i s t i c i anwi l lof t e ns e l ec tanunbi as e ds t a t i s t i co ve rabi as eds t a t i s t i c .Bas e don wha tyoul e a r ne d,whymi ghts t a t i s t i c i a nspr e f e runbi as eds t at i s t i c s ? Fr om whatIhavel e ar ne d, anunbi as eds t a t i s t i cwoul dbepr ef er r edove rabi as e donebec aus ei tc r eat esafinal a ns wert hati sc l os e rt ot hepur egues s . Al s o,i tc r e a t esr e aldat at hathasnotbe ent ampe r e dwi t huponbi as ....