Inventory of plant material in forest nurseries by combining an ocular estimate and sampling measurements

Size: px
Start display at page:

Download "Inventory of plant material in forest nurseries by combining an ocular estimate and sampling measurements"

Transcription

1 JOURNAL OF FOREST SCIENCE, 48, 00 (4): Ivetor of plat material i foret urerie b combiig a ocular etimate ad amplig meauremet ¼. ŠMELKOVÁ Techical Uiverit, Facult of Foretr, Zvole, Slovak Republic ABSTRACT: Two procedure of the plat material ivetorie i foret urerie, ued util ow, are evaluated: ocular etimate ad amplig. A ew two-phae amplig procedure ha bee propoed o the bai of a uitable combiatio of etimatio ad coutig ad/or meauremet of eedlig ad plat. The optimum ize of the amplig uit (legth of bed egmet) ha bee defied. The ecear umber of bed egmet o which the ocular etimatio hould be performed i the firt phae ( ), ad ubequetl a more exact aemet of the umber of idividual ad/or their other qualitative ad quatitative trait hould be doe i the ecod phae ( ), to achieve the required preciio of reult of ± to 0 with reliabilit of 95. A theoretical jutificatio of the propoal a well a a detailed procedure of the accomplihmet i preeted. The frame have bee pecified where the propoed method i ecoomicall twice a beeficial a the claic amplig method. Keword: foret urerie; plat material ivetor; two-phae amplig method; combiatio of ocular etimate ad exact aemet PROBLEM I foret urerie i Slovakia ad imilarl i other coutrie, where the urer tock i cultivated iteivel, ome te millio eedlig ad plat of variou tree pecie are produced auall repreetig a great material ad fiacial value. It i therefore quite atural that the ubject providig ad cotrollig thi productio are ot ol obliged to etimate both the quatit ad the qualit of the cultivated urer tock a objectivel a poible but alo the are itereted i thi proce. Both thee characteritic how a relativel high variabilit depedig o ma factor, uch a local coditio of urerie, qualit of the eed ued, cultivatio techique, kid ad age of the cultivated urer tock, weather coditio, occurrece of oxiou aget, etc. Obvioul, foret urerie produce a great umber of eedlig ad plat ad therefore the whole-area ivetor of the urer tock (e.g. coutig, height meauremet, aemet of the health tate of all idividual i a urer) would ot be ecoomicall feaible. Due to thi fact, the two followig method ca be coidered: qualified etimatio or a appropriate amplig method. The preet paper give a evaluatio of the tatu quo ad practical applicatio of the two above-metioed method of the urer tock ivetor i Slovakia ad i the eighbourig coutrie ad propoe a ew method baed o the combiatio of a ocular etimate ad amplig procedure. Preeted reult were obtaied from the olutio of VEGA/7056/0 Reearch project. EXPERIMENTAL MATERIAL The experimetal material come from experimetal plot of the Drakšiar foret urer, foret office Beòuš. The were etablihed i uch a wa that would make it poible to follow all the baic apect of the urer tock ivetor i more variat. The reearch material iclude 0 categorie of eedlig ad plat: pruce: +0, +0, +, +, +3, +/, larch: +0, +0, beech: +0, +0. Seed bed from 00 to 300 m i legth were choe for each categor. A woode frame with the ier dimeio of 46 cm ( eed bed width) 00 cm wa made for the proper etimatio. The horter ide wa divided ito four 5 cm-log egmet b mea of the wire. The frame wa cotiuoul placed alog the whole eed bed ad withi each of the 5 cm-log egmet, the umber of plat b coutig ad etimate a well a the mea plat height b meaurig ad etimate were determied. The time eeded for idividual performace wa recorded (i mi). Thi data bae repreetig the baic et for each ivetigated categor of plat material wa the bai to create ew data for the eed-bed egmet of differet legth (5, 50, 75,... 75, 00 cm) ad repeated amplig of a maller amout of egmet i differet combiatio wa performed. I thi wa, the ivetigatio became 56 J. FOR. SCI., 48, 00 (4): 56 65

2 more effective ad objective becaue the differece betwee the amplig procedure ad the ocular etimate compared with the correct value could be uambiguoul determied for the whole eed bed eve for more ivetigated alterative. EVALUATION OF CURRENTLY USED INVENTORY METHODS OCULAR ESTIMATE Thi i the oldet ad curretl the mot frequetl ued method (Guidelie of the Miitr of Foretr ad Water Maagemet from 975; KANTOR et al. 975). At everal place of a foret urer the umber of idividual i etimated per ruig metre of the eed bed ad the reult i calculated for the etire area (legth) of the eed bed. Other trait of the urer tock are etimated imilarl, e.g. qualit cla, percetage of damage, etc. Such ocular etimate i ver fat ad cheap but it ca coiderabl be loaded b the etimator ubjective ifluece. The magitude of the etimatio error i ot kow ad it ha ot bee tudied either i our coutr or abroad. The firt reult cocerig the accurac of the ocular etimate were obtaied from the evaluatio of our experimetal material. It ha bee how that eve after a ver qualified etimatio (for reearch purpoe), the egative tematic error prevail ad repreet.55 i the cae of the umber of plat ad.55 a for the height of plat. I curret practice, the ca be much greater. Thi problem i dealt with i greater detail i the paper b ŠMELKOVÁ (998). SAMPLING METHOD It belog to ewer ad more objective procedure baed o the priciple of mathematical tatitic. From the reult obtaied from a mall umber of ample, the cocluio ca be draw for the whole foret urer. A part of the eed bed, e.g. oe metre of eed bed or a area of m, i choe a a ample or a amplig uit. Thee are the evel ditributed over all eed bed. I each of the uit, the repective value of the determied variable i foud, e.g.,,... (umber of plat, mea height of plat) ad the ample arithmetic mea i calculated. i i () It i the ued to determie the umber of plat Y, or the mea height of plat Y of all the urer tock of a give categor i a foret urer accordig to the followig relatio: Y N ± Y () Y ± Y (3) where N i umber of all poible amplig uit, i.e. the etire legth i ruig metre or area i m of the repective ivetoried eed bed. Y or Y i amplig error ad defie the rage the real differece betwee the ample reult ad the correct oe doe ot exceed with 95-probabilit. It i calculated accordig to the followig formula: where Y N ad/or ( i ) i i Y (4) i i i tadard deviatio of ample value i (abolute variabilit rate) ad i umber of all ample. I cae that i formula (4) i ubtituted b the coefficiet of variatio ( / ). 00, the relative error Y or Y i obtaied i percet. Compared with ocular etimate, the decribed amplig method i more profeioal ad time-coumig; everthele, it ha the advatage of beig more repreetative (objective); furthermore, the cofidece iterval ca be added to the obtaied reult ad if the required accurac i give before, the rage of amplig etimatio ca be plaed o that the total ivetor will be carried out with the miimum cot. The amplig priciple of the plat material ivetor were elaborated i detail i Germa (SCHUBERT, HOL- LENDER 986; SCHUBERT 987). I the Czech Republic, ome origial uggetio reulted i a tadardized methodical itructio for the applicatio i practice (NO- VOTNÝ 965; PÁV et al. 990; PÁV 99). I Polad, SOB- CZAK et al. (99) cotributed to the problem olutio. However, all curretl ued amplig procedure uffer from ome methodical drawback a the are baed o geeral data o the urer tock variabilit ad the amplig etimatio i a urer i aimed at jut oe amplig uit ize ruig metre, m or eve at a eed bed of ruig metre (i Germa). The experiece from our experimet eable to appl a much more varied approach to plaig ad carrig out the amplig ivetor with regard to particular coditio i a foret urer. It ha bee how that itead of the amplig uit ( ruig metre, m ) recommeded util ow, it i much more advatageou to ue a maller amplig uit a eed bed block d 5 cm; for eedlig with a high deit of idividual ol oe half or oe quarter of that block. Such a uit eem to be optimal from the poit of view of accurac ad ecoom of etimatio. Thi i alo proved b the data i Table. Determiatio of the umber of pruce plat ad larch eedlig with the required accurac E ± 5 ad reliabilit P 95 i carried out o the choe hort uit d 5 cm i legth with a higher umber of amplig uit o the oe had, but coiderabl lower total cot tha it i with 00 cm-log amplig uit o the other i J. FOR. SCI., 48, 00 (4):

3 Table. The effect of bed egmet of differet legth (a 5 cm, b 00 cm) o primar parameter of amplig determiatio of the umber of plat ad eedlig with requeted preciio E ± 5 Number of Variatio Required Time Plat idividual coefficiet ample ize cot material T Idexe a:b for: a b a b a b a b T Plat pruce Seedlig larch , had. Correpodig rate of relative variabilit were derived for amplig uit defied i thi wa coefficiet of variatio of the umber ad mea height of plat ad eedlig. It ha bee foud that the value rage withi a coiderabl great iterval from 0 to 45 ad the ca be relativel eail determied before the etimatio begiig for ever foret urer ad categor of plat material b mea of the ocular judgemet of the deit ad height variabilit of the idividual o the eed bed area. I geeral, the coefficiet of variatio of plat umber i lower (5 0) tha that of eedlig (30 40) ad the variabilit of mea height betwee the eed bed block i approximatel /3 of the variabilit of the umber of idividual. The rage of the amplig etimatio deped o the variabilit of plat material. Thi i the reao wh Table give umber of eed bed block (with a legth of d 5 cm) to the expected mea value. The eed bed block mut be choe o that the amplig reult with the error ot exceedig the cofidece limit of E 95 will be reached. The obtaied kowledge i recorded i greater detail ad verified i practical applicatio i the paper b ŠMELKOVÁ (996, 997). PROPOSAL OF A NEW METHOD BASED ON THE COMBINATION OF OCULAR ESTIMATE AND CONTROL MEASUREMENT BASIC PRINCIPLE OF THE METHOD Thi method i baed o a ew priciple of the twophae ample urve recetl applied more frequetl with great advatage i foretr, e.g. i foret ivetor, terretrial urveig ad where a complicated variable ca be determied b aother oe that i determied more eail ad i i cloe correlatio to the reultig variable. The theor of the method wa decribed b DE VRIES (986) ad SHIVER ad BORDERS (996) ad for the applicatio i foretr it wa elaborated i everal variat b ŠMELKO (990). It applicatio to urer tock make it poible to implif ad ecoomize the precedig ample urve. The whole procedure ca be divided ito two phae. I the firt phae, the etimated variable umber of plat or their mea height i determied o eed bed block Table. Required ample ize () for differet accurac of plat ad eedlig umber ad the average height etimate at a reliabilit of 95 ad expected variatio coefficiet ( ) of the ivetoried plat material for E ± ± 5 ± 0 ± , , b the ocular etimatio from which approximate (etimated) value o are obtaied. I the ecod phae, a maller part of eed bed block i choe from the eed bed block ad the repective variable i determied out of them i a more precie wa b coutig or meaurig. For thee block, the matched pair of the plat umber or their mea height (x o etimated ad x M couted or meaured) are obtaied. Thee are the ued for correctio (preciio) of all the etimated value o. The correctio ca be carried out i everal wa. Theoreticall, mot appropriate would be the regreio etimate b mea of which the regreio equatio x M f(x o ) i calculated from the data of x o ad x M ad after ubtitutio of O for x O the more precie value Y i derived. However, the calculatio are relativel complicated. The ratio etimate would be eaier where the preciio i reached b mea of the ratio xm R o that Y R O. There are two x O baic coditio, i.e. the depedece x M ad x o mut pa through the begiig of coordiate ad the variabilit x M hould grow proportioall with the icreaig value x o which our experimet did ot however cofirm uambiguoul. Therefore, o-called lit amplig i recommeded for our eed. Although it expect the approximate etimatio of the value o o all populatio uit (i.e. o all urer eed bed block with a legth of 58 J. FOR. SCI., 48, 00 (4): 56 65

4 d 5 cm) ad amplig with uequal probabilitie, which i difficult to appl reaoabl i the ivetor of urer tock, however if modified, it give earl the ame reult a the regreio etimatio ad i much more advatageou for practical applicatio. For the evaluatio of the data o, x o, x the followig tep are required. m For each pair of the value x o, x M the quotiet q i are calculated x M ( i) q i (5) xo( i) ad their baic tatitical characteritic (mea value q, tadard deviatio q ad coefficiet of variatio q ): q i q i q qi qqi i i q q 00 (6) q The etimated value o are corrected accordig to the relatio Y O q O( i) i O (7) The amplig error of the corrected value Y (for the reliabilit of 95) i determied i percet ad i abolute value O + q Y (8a) Y Y Y (8b) 00 where i the coefficiet of variatio calculated from etimated value of O(i). The other mbol are alread kow. The firt expreio uder the root repreet the error due to ocular etimatio, the ecod give the error reultig from a mutual relatio betwee the etimated ad preciel determied data x O ad x M. The total error Y defie the limit which the real differece of the corrected value a agait to the correct ukow (however exitig) value Y doe ot exceed with probabilit of 95. The iterval i derived withi which the real total umber of the give categor of eedlig ad plat Y or their real mea height Y i to be expected with probabilit of 95. Y D ( Y ± Y ) d Y Y ± Y (9) NECESSARY INPUT DATA AND THE METHODS OF THEIR ACQUISITION It follow from the above metioed that before the propoed procedure i ued, it i ecear to decide o the umber of eed bed block ad o which the repective variable o, x o, x M are to be etimated. Thi quetio ca be awered b derivig ad from equatio (8a) for the modulu of preciio Y of the whole urve give i advace. However, it preuppoe to roughl kow the expected variabilit of ocular etimate of the variable O a well a the variabilit of the quotiet q ( q ). Both thee characteritic deped o the qualit of ocular etimate. Good-qualit etimate are coidered thoe that are more table, le variable i pite of the fact that the have a tematic deviatio (at each etimatio b 5). It i ol importat for them to have a low variabilit approachig their mea value ( O ) ad to how the cloet poible correlatio with the meaured value. The the low coefficiet of variatio q will be obtaied. A tematic deviatio of the etimatio from the correct value i le dagerou becaue uig the propoed method, it ca eail be elimiated b correctig the etimatio b mea of the mea value of the quotiet q (accordig to equatio [7.]). Of coure, the rage of ample urve of ad i determied b the expediture o etimatio ad meauremet to be carried out. All the give iput variable were derived from our experimetal material, the reult of which were the followig geeral fidig (Table 3, Fig. ): Coefficiet of variatio for the etimatio (O) i all examied categorie of urer tock coicide well i both the umber of idividual ad the mea height with the coefficiet of variatio for the meaured data S x(m) ad i ma cae, it i eve lower. Coefficiet of variatio q expreig the variabilit of the ratio of meaured ad etimated value rage from 0 to 3 ad it i alwa lower tha that of the meaured value. It repreet ol / or /3 of their value. Correlatio coefficiet of the liear correlatio betwee meaured ad etimated value r M/O i urpriigl high (0.85), provig a ver cloe correlatio approachig the ideal fuctioal relatio whe r.00. Workig time (T) eeded for coutig plat ad eedlig icludig the meauremet of their mea height ver much deped o the umber of idividual () o a eed bed block. It icreae imultaeoul with the time coumptio i a curviliear wa accordig to the followig equatio: T (0) where the correlatio idex of thi depedece reache the value I T The time eeded for etimatig the plat umber i o average 5 time horter ad that for etimatig the eedlig umber approximatel 0 time horter. From the above give time coumptio, a ubtatial part (about 80 or 90) i devoted to determiatio of the umber of idividual; meauremet ad height etimatio i le time coumig becaue it i aimed at fidig the average idividual rather tha all idividual i the eed bed block. J. FOR. SCI., 48, 00 (4):

5 Table 3. Characteritic of the relatio betwee the etimated ad meaured idicatio for the umber ad average height of plat ad eedlig o bed egmet d 5 cm i legth Size q M/O Q (o) (m) Etimate Sizig r M/O Number of plat Height of plat Number of eedlig Height of eedlig etimatio-meaurig procedure of, with the oephae procedure baed ketirel o a meauremet give i Table of the precedig chapter, we will fid that i the cae of low variabilit of the urer tock ( ) ad high preciio (E ), the total cot at two-phae procedure eem to be more ufavourable tha at oe-phae procedure. Therefore, i Table 4 a bold lie defie the area i which the two-phae combiatio of etimatio ad meauremet i more advatageou, wherea outide thi area, a oe-phae procedure of direct urve (without etimatio) i recommeded. Fig.. Necear time for coutig the umber of plat ad eedlig (T i mi) i depedece o the umber of idividual () o bed egmet of legth d 5 cm The required umber of eed bed block for the firt phae ad for the ecod phae of the ivetor i calculated from the acquired iput data for differet variabilit degree of the umber of plat ad eedlig for differet required preciio E of the total amplig reult give i Table 4. I calculatio, the data o variabilit (O) ad q, correlatio r M/O, ad o the mutual proportio of total cot T for etimatio ad meauremet were coidered. The were applied i formula for plaig the regreio two-phae amplig but the are ot preeted here becaue of their complexit. The ca be foud i the paper: SHIVER ad BORDERS (996, pp ). If we compare the rage of ample urve for the two-phae DIRECTIONS FOR THE APPLICATION OF THE METHOD IN PRACTICE The method ha bee deiged to be applied impl ad uambiguoul i practice. For plaig the optimal procedure it i ecear to: Carr out the ocular etimate of urer tock, mark off the eed bed accordig to the categorie (pecie, age, plat, eedlig) ad ae the variabilit degree ( ) of the umber of idividual betwee the uppoed amplig uit (eed bed block). Chooe the required ivetor preciio E applig the geeral priciple that higher preciio (maller error) hould be ued for rare pecie ad a great amout of urer tock of high qualit (where eve a mall relative error repreet the abolute great value, e.g. E ± repreet 0,000 idividual at oe millio plat) ad o the cotrar, lower preciio will do for the lower-qualit, cheaper, eail acceible material, jut for radom ivetor. Table 4. Required umber of bed egmet o which it i ecear to make both the ocular etimate ( ) ad coutig, or meauremet ( ) of plat material i depedece o the expected variabilit ( ) ad required preciio (E) of the ivetor reult uig a combied method E ± E ± 5 E ± , , Note: I cae limited rude lie i combied method ecoomic twice preferable tha claic uperior method 60 J. FOR. SCI., 48, 00 (4): 56 65

6 Table 5. Example of the realiatio of a combied method i foret urer. Size detectig: Y umber of Norwa pruce plat (+), total bed legth D 300 m, expected variabilit 0, required preciio E ± 0, elected bed elemet d 5 cm, ample ize for ocular etimate 30, coutig the umber 0 xm ( i) Segmet No. Etimate O(i) Coutig x M(i) q i Auxiliar calculatio: xo( i) O(i) 3 0 O ( i ) 5, O , ,.5(675) ( o) ( o) q i i q q, (0.87) q q Etimate correctio ad all bed geeralizatio Y Y q, pc pc O ( O) q ± 7.9 Y ( Y ± Y ) ( 4.46 ±.93) 9,33 ±,36 pc Y Y Y ±.93 pc D d pc J. FOR. SCI., 48, 00 (4):

7 Chooe the ize of a amplig uit which i i geeral a eed bed block d 5 cm i legth for plat (for ettig out the plat uder 5 idividual, the block hould be prologed to d 50 cm), for eedlig with deit up to 00 idividual the eed bed block with a legth of d 5 cm hould be ued, wherea the origial eed bed block hould be reduced to oe half or eve oe quarter i the cae of higher deit. Take from Table 4, for the give variabilit ad choe error E, the ecear amout of eed bed block for ocular etimate ad for coutig the idividual. If their height ivetor i take imultaeoul, the mea height do ot have to be determied o all ad eed bed block, jut o approximatel / or /3 of them a the mea height variabilit of urer tock o the eed bed block i ubtatiall lower tha that of their umber. To calculate the ditace for equal pacig of amplig uit alog the eed bed o which the etimate will be performed where: D total legth of eed bed D () ad the tep for amplig uit will be determied from the ratio k ; o amplig uit, both the etimate ad the coutig or meaurig of the height of idividual will be carried out. For carrig out the meauremet it i ecear to: Make a light woode frame with ier dimeio of eed bed width 5 cm ad for providig the ivetor of eedlig with high deit to tretch a wire i vertical directio i the half ad alo i the quarter of the loger frame ide. Place the frame alog the eed bed at ditace ; the firt locatio hould be doe at a ditace of / from the begiig of the eed bed, the other at a ditace of the whole ; to do ocular etimatio o all locatio ad o each k th of them alo a precie coutig ad meaurig of the idividual. The ditace ca be meaured b mea of a tape meaure or tep. Make a record of the reult obtaied from the ucceive locatio i,, i two colum o that the meaured value x M(i) form pair with the etimated value O(i) o idividual locatio. Evaluate the obtaied data accordig to formula (5 9); to calculate the quotiet q i ad their tatitical characteritic for the pair value x M(i) ad x O(i) ; to determie the mea etimated value O(i) of the umber or height of urer tock ad correct it b mea of q, to calculate the amplig uit for the whole ivetoried eed bed ad to tate the rage of the reached preciio. Table 5 give oe example of a record ad data evaluatio of the ivetor of pruce plat + b mea of the propoed combied method o a eed bed legth D 300 m, etimated variabilit 0, choe preciio E ± 0, rage of amplig for ocular etimate 30 ad for coutig 0, choe amplig uit (legth of amplig block) d 5 cm, ditace for locatio (etimatio) 300/30 0 m, amplig tep for locatio (coutig) k 30/0 3 (each third from locatio i the ucceio, 5, 8, 9). It follow from the reult that the mea etimated umber of plat o 30 locatio i O.5 ad the relative variabilit of idividual etimate i (O) 5.7. The mea value of the precie coutig of idividual o 0 locatio i higher x M 3.7 ad their variabilit X(M) 7.8 ha alo icreaed. Mutual relatio betwee the etimated ad couted umber of plat i expreed b the coefficiet q i ad it rage from ad.3. It mea value i q.087. It mea that the umber of plat obtaied b coutig were o average b 8.7 higher tha the etimated oe; the ocular etimate uderetimated the real tate tematicall. The variabilit of q i value i ver low, q 8.7 ad it decreaed.8 time i compario with (O) of the etimated value ad.0 time i compario with X(M) of the couted value. It mea that there i a ver cloe correlatio betwee the etimate ad coutig, eve i pite of the fact that the etimate how a tematic deviatio ad are predomiatl maller. After a correctio b mea of q, the origiall etimated mea umber of plat o the 5 cm-log locatio O icreaed ad repreeted Y plat; after calculatio for the whole legth of D 300 m of the ivetoried eed bed it repreet Y /0.5 9,35 plat. The relative amplig error of the corrected reult i Y ± 7.9. It mea that with 95 probabilit the total umber of plat o eed bed rage withi the iterval of 9,35 ±,36 piece of plat, i.e. from 7,036 to 3,668 idividual. If we eeded a more precie reult, it would be ecear to ehace the rage of ample urve of,, for the required E ± 5 o 05, 35 eed bed block. Beide howig the whole procedure of evaluatig the obtaied data ad the iterpretatio of the reult, the above give example alo cofirm that plaig ad carrig out the two-phae ivetor wa correct. The coefficiet of variatio for the etimatio (O) 5.7 wa eve lower tha origiall expected (0) ad the error of the ivetoried umber of a repective categor of plat i a urer Y ± 7.9 did ot exceed the required rage of E ± 0 (it repreeted ol 79). A the example wa applied o a eed bed where (for the ake of ivetigatio) the precie umber of plat b coutig o all eed bed block (Y 9,04 plat) wa alread kow before, it wa poible to determie the real error of the corrected amplig reult 9,35 9, plat, i.e If the ocular etimate of the umber of plat (Y O /0.5 7,000) were ot corrected i the ecod phae of ivetor, the real error of determiig the correct value would be 7,000 9,04,04 plat, i.e. eve J. FOR. SCI., 48, 00 (4): 56 65

8 SUMMARY It follow from the previou chapter that at preet three method of the ivetor of plat material i foret urerie are ued. Each of them ha it ow advatage ad diadvatage. The ocular etimatio of plat ad eedlig umber, or alo of ome other characteritic, e.g. damage, mea height, i cheap, however it accurac i ot kow ice it deped o the ubjective propertie of the etimator ad i uuall loaded b tematic error (ŠMELKOVÁ 998). Claical amplig replacig the ocular etimatio b a direct ivetor (coutig, meaurig) of the plat material at everal place tematicall ditributed o all eed bed i more objective. It utilie the theor of tatitical amplig ad for the aumed variabilit of plat material (which ca eail be judged accordig to the degree of deit variabilit ad other parameter of plat ad eedlig o eed bed) it make it poible to etimate the requeted umber of (place) meauremet o eed bed to ecure the ivetor reult with a give accurac of e.g. ±, ± 5 or ± 0 (Table ). After carrig out the ivetor, the amplig reult i derived from the meauremet (e.g. umber of idividual i the give categor, percetage of damage, mea height, etc.) i the form of the reliabilit iterval defied b the lower ad upper limit, i which the real (exact) value i the total ivetoried part of the foret urer repreet 95 probabilit. Thi procedure, however, require higher techical kill of worker ad 5 to 0 time higher cot tha the ocular etimatio. The preet methodological procedure (ŠMELKOVÁ 996) ha bee elaborated to uch a extet that it i ea to be maaged i the curret urer practice without a prelimiar theoretical preparatio. The propoed two-phae amplig procedure combie the advatage of ocular etimatio ad direct ivetor. It follow from the theor of regreio amplig, which i the firt phae determie quickl ad cheapl, although le preciel, the required characteritic b the ocular etimatio o a higher umber of amplig uit ( ), ad i the ecod phae o a maller umber ( ) of amplig uit eve more preciel b coutig or meauremet. From data, the idividual proportio of the meaured ad etimated value of the ame characteritic are calculated ad their value (multiplicatio quotiet q) i ued for the correctio of all etimated ad meaured data (the correlatio coefficiet i plat i about 0.85 ad i eedlig about 0.95). Thi fact i favourabl reflected i the error (the iterval of reliabilit) of the correct reult ad the ecoom of the etire ivetor. A it i ee from Table 3, for eurig the requeted accurac E (±, ± 5 or ± 0) at the give variabilit of plat material (0 40), the umber of the required ocular etimate icreae i compario with the claical amplig procedure while the umber of the required direct etimate ubtatiall decreae. Total time coumptio ecear for thi combied ivetor i reduced b 50. The whole workig procedure i quite imple, calculatio of the required formula (5 9) are ot difficult; the ca eail be carried out uig a pocket calculator, bet of all the cietific tpe (example i Table 4). For the ake of completee it i ecear to metio that i the preeted work, for all three above-metioed ivetor variat, the optimum amplig uit were defied i a ew wa o the bai of large ample to which both the ocular ad the direct ivetorie refer. Itead of m or m of the eed bed ize it i recommeded to ue a maller ad more variable uit with a legth of 5 cm of the eed bed, or with a higher deit of idividual mail eedlig, / or /4 of thi ditace. The required accurac i thu provided at miimum cot (Table ). Light woode frame are bet uited for the etablihig of uch a amplig uit that i placed alog the ivetoried eed bed at cotat ditace ( total legth of eed bed/umber of eed bed legth ). There i o igle repl to the quetio which of thee method i the bet oe. It deped o the ivetor aim ad o the tpe ad quatit of platig material. The direct ocular etimatio hould be retricted ol to acquiitio of rough orietatio iformatio. I commo practice, the claical amplig or combied amplig method of ivetor ad meauremet hould be preferred. The latter i twice a effective (epeciall at a variabilit higher tha 0). The required ivetor accurac hould be elected withi the rage from ± to ± 0 with the aim to ivetor more exactl the material that occur i large quatitie ad that i of higher value (qualit ad price). Referece DE VRIES P.C., 986. Samplig Theor for Foret Ivetor. Wageige, Berli, Spriger Verlag: 4. KANTOR J. et al., 975. Zakládaí leù. Praha, SZN: 56. KOLEKTÍV, 975. Smerice è. 57/0 a zakladaie a obhopodarovaie leých škôlok. Bratilava, MLVH SSR: 7. NOVOTNÝ M., 965. Jeda z metod ivetarizace azeic ve školkách. Le. Práce, 44: PÁV B., MICHALEC M., BÌLE J., 990. Metodický pok pro ivetarizaci emeáèkù a azeic. Le. Prùv., Jílovištì-Strad, VÚLHM: 40. PÁV B., 99. Staoveí záob adbového materiálu a plochách školk. Leictví, 37: SHIVER B.D., BORDERS B.E., 996. Samplig Techique for Foret Reource Ivetor. New York, Joh Wile ad So: 356. SOBCZAK R. et al., 99. Szkolkartwo leœe. Warzawa, Wdawictwo Swiat: 9. SCHUBERT J., 987. Iveturverfahre für die Pflazevorräte i Fortbaumchule. Beitr. Fortwirtch., : 4. SCHUBERT J., HOLLENDER H., 986. Eiheitliche Iveturverfahre für die Pflazevorräte i Fortbaumchule. Berli, Soz. Fortwirtch., 36:. ŠMELKO Š., 990. Zi ovaie tavu lea kombiáciou odhadu a meraia dedrometrických velièí. Vedecké a pedagogické aktualit. Zvole, VŠLD, ES: 88. J. FOR. SCI., 48, 00 (4):

9 ŠMELKOVÁ ¼., 996. Ivetarizácia adbového materiálu v leých škôlkach výberovým pôobom. Leíck èaopi Foretr Joural, 4: ŠMELKOVÁ ¼., 997. Experimetále overeie výberového pôobu zi ovaa poètu adeíc v leých škôlkach. Acta Fac. For., XXXIX: 6 7. ŠMELKOVÁ ¼., 998. Poúdeie okuláreho odhadu poètu a výšk adeíc v leých škôlkach Acta Fac. For., XL: 9 7. Received 8 Februar 00 Ivetarizácia adbového materiálu v leých škôlkach kombiáciou okuláreho odhadu a kotrolého meraia ¼. ŠMELKOVÁ Techická uiverzita, Leícka fakulta, Zvole, Sloveká republika ABSTRAKT: V práci a hodotia dva doteraz používaé pôob ivetarizácie adbového materiálu v leej škôlke okulár odhad a výberová metóda. Navrhuje a ový dvojfázový výberový potup, založeý a vhodej kombiácii odhadu a poèítavaia, rep. meraia emeáèikov a adeíc. Defiuje a optimála ve¾ko výberovej jedotk (dåžka záhoového úeku). Odvodzuje a potrebý poèet záhoových úekov, a ktorých treba vkoa v prvej fáze ( ) okuláre odhad a úèae v druhej fáze ( ) aj preejšie ziteia poètu jedicov, rep. ich ïalších kvalitatívch a kvatitatívch zakov, ab a doiahla požadovaá preo výledku ± až 0 o po¾ahlivo ou 95. Predkladá a teoretické zdôvodeie ávrhu i kokrét pracový potup jeho realizácie. Vmedzujú a rámce, ked je avrhovaá metóda ekoomick (až dvojáobe) výhodejšia ako klaická výberová metóda. K¾úèové lová: leé škôlk; ivetarizácia adbového materiálu; dvojfázová výberová metóda; kombiácia okuláreho odhadu a preého zi ovaia V úèaoti ú pre ivetarizáciu adbového materiálu v leých škôlkach k dipozícii tri rôze pôob, ktoré majú voje výhod i evýhod. Okulár odhad poètu adeíc a emeáèikov, rep. aj iektorých ich ïalších zakov (apr. poškodeia, priemerej výšk) je rýchl a lacý, ale ie je záma jeho preo, lebo ve¾mi závií od ubjektívch vlatotí odhadcu a pravidla je za ažeý tematickými chbami (ŠMELKOVÁ 998). Klaická výberová metóda, ktorá ahrádza okulár odhad priamm zi ovaím (poèítaím, meraím) adbového materiálu a viacerých mietach rozložeých pravidele po všetkých ivetarizovaých záhooch, je objektívejšia. Vužíva teóriu štatitického výberu, takže pre predpokladaú variabilitu adbového materiálu (ktorá a dá dobre poúdi pod¾a tupòa premelivoti hutot a iých parametrov adeíc a emeáèikov po záhooch) umožòuje taovi potrebý poèet (miet) meraí a záhooch tak, ab a zabezpeèil výledok ivetarizácie vopred zvoleou požadovaou preo ou, apr. ±, ± 5 alebo ± 0 (tab. ). Po vkoaí zi ovaia a zo zíkaých údajov odvodí výberový výledok (možtvo jedicov daej kategórie, perceto poškodeia, priemerá výška ap.) vo forme tzv. itervalu po¾ahlivoti, vmedzeého podou a horou hraicou, v ktorom kutoèá (preá) hodota v celej ivetarizovaej èati leej škôlk leží 95 pravdepodobo ou. Samozrejme, že to vžaduje vššiu odboro a 5 0-krát väèšie èaové áklad ako okulár odhad. Súèaý metodický potup je však už ato¾ko prepracovaý (ŠMELKOVÁ 996), že je ve¾mi ¾ahko zvládute¾ý v bežej škôlkárkej praxi aj bez predchádzajúcej teoretickej príprav. Navrhovaá dvojfázová výberová metóda pája výhod okuláreho odhadu a priameho zi ovaia v ich vzájomej kombiácii. Vchádza z teórie regreého výberu, ktorý v prvej fáze a väèšom poète výberových jedotiek ( ) taoví zi ovaú velièiu rýchlo, laco, ale meej pree okulárm odhadom a v druhej fáze a mešom poète ( ) týchto jedotiek aj preejšie poèítavaím, rep. meraím. Z údajov a vpoèítajú vzájomé podiel odmeraej a odhadutej hodot tej itej velièi a ich priemer (áobý kvociet q) a použije a ekciu všetkých odhadutých hodôt. Tým a odtrái prípadá tematická chba v okulárch odhadoch a zároveò a podtate zíži variabilita výledkov, pretože medzi odhadutými a meraými údajmi exituje ve¾mi teá 64 J. FOR. SCI., 48, 00 (4): 56 65

10 elácia (elaèý koeficiet pri adeiciach je okolo 0,85 a pri emeáèikoch 0,95). To a priazivo prejaví a chbe (ve¾koti itervalu po¾ahlivoti) igovaého výledku a tiež a ekoomike celého zi ovaia. Ako vidie z tab. 3, pre zabezpeèeie požadovaej preoti ivetarizácie E (±, ± 5, ± 0 ) pri predpokladaej variabilite adbového materiálu (0 40 ) a v porovaí klaickou výberovou metódou potrebý poèet okulárch odhadov o ieèo zvýši, ale poèet priamch zi ovaí a podtate obmedzí. Celkový èaový áklad a vkoaie kombiovaej metód ivetarizácie a preto zíži v priemere a polovicu. Celý pracový potup je pritom pomere jedoduchý, výpoèt potrebých velièí pod¾a vzorcov (5 9) ie ú ároèé, dajú a ¾ahko zvládu a vreckovej kalkulaèke, ajlepšie tpu Scietific (príklad v tab. 4). Pre úplo treba pozamea, že pre všetk tri pomíaé variat ivetarizácie boli v práci a základe roziahlch rozborov ovým pôobom defiovaé aj optimále výberové jedotk, a ktoré a okuláre odhad aj priame zi ovaie vz ahuje. Namieto jedotej ve¾koti (doteraz m alebo bm záhou) a odporúèa používa mešia a variabilejšia jedotka, a to záhoový úek o dåžke d 5 cm, rep. pri väèšej hutote jedicov (ajmä emeáèikov) polovica alebo štvrtia tohto úeku. Tým a zabezpeèí požadovaá preo výledku miimálmi ákladmi (tab. ). Na vmedzeie takejto výberovej jedotk a ajlepšie hodí ¾ahký dreveý rám, ktorý a ukladá pozdåž ivetarizovaých záhoov v koštatých odtupoch ( celková dåžka záhoov/ poèet záhoových úekov ). Na otázku, ktorý z troch pôobov ivetarizácie použi, ejetvuje jedozaèá odpoveï. Závií to od úèelu zi ovaia a od druhu a možtva adbového materiálu. Èitý okulár odhad b a mal obmedzi iba a zíkaie hrubých, orietaèých iformácií. Beže b a mala v praxi preferova klaická výberová metóda alebo ešte viac kombiovaá metóda odhadu a meraia, ktorá je (ajmä pri variabilite väèšej ako 0 ) až dvakrát efektívejšia. Pritom požadovaá preo ivetarizácie b a mala voli z rozpätia ± až ± 0 tak, ab a preejšie podchtil materiál, ktorý a v škôlke vktuje vo ve¾kom možtve a má väèšiu hodotu (kvalitu a ceu). Correpodig author: Prof. Ig. ¼UBICA ŠMELKOVÁ, CSc., Techická uiverzita, Leícka fakulta, T. G. Maarka 4, Zvole, Sloveká republika tel.: , fax: , J. FOR. SCI., 48, 00 (4):

Confidence Intervals for Linear Regression Slope

Confidence Intervals for Linear Regression Slope Chapter 856 Cofidece Iterval for Liear Regreio Slope Itroductio Thi routie calculate the ample ize eceary to achieve a pecified ditace from the lope to the cofidece limit at a tated cofidece level for

More information

Topic 5: Confidence Intervals (Chapter 9)

Topic 5: Confidence Intervals (Chapter 9) Topic 5: Cofidece Iterval (Chapter 9) 1. Itroductio The two geeral area of tatitical iferece are: 1) etimatio of parameter(), ch. 9 ) hypothei tetig of parameter(), ch. 10 Let X be ome radom variable with

More information

TI-83, TI-83 Plus or TI-84 for Non-Business Statistics

TI-83, TI-83 Plus or TI-84 for Non-Business Statistics TI-83, TI-83 Plu or TI-84 for No-Buie Statitic Chapter 3 Eterig Data Pre [STAT] the firt optio i already highlighted (:Edit) o you ca either pre [ENTER] or. Make ure the curor i i the lit, ot o the lit

More information

Quantization and Analog to Digital Conversion

Quantization and Analog to Digital Conversion Chapter 10 Quatizatio ad Aalog to Digital Coverio I all thi cla we have examied dicrete-time equece repreeted a a equece of complex (ifiite preciio) umber. Clearly we have bee dicuig implemetatio of may

More information

Stratified random Sampling. Application for Remote Sensing investigations

Stratified random Sampling. Application for Remote Sensing investigations Stratified radom Samplig Applicatio for Remote Seig ivetigatio Samplig Populatio: te etire group uder tud a defied b reearc objective Sample: a ubet of te populatio tat ould repreet te etire group Sample

More information

Determining the sample size

Determining the sample size Determiig the sample size Oe of the most commo questios ay statisticia gets asked is How large a sample size do I eed? Researchers are ofte surprised to fid out that the aswer depeds o a umber of factors

More information

Confidence Intervals for One Mean

Confidence Intervals for One Mean Chapter 420 Cofidece Itervals for Oe Mea Itroductio This routie calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) at a stated cofidece level for a

More information

1 Correlation and Regression Analysis

1 Correlation and Regression Analysis 1 Correlatio ad Regressio Aalysis I this sectio we will be ivestigatig the relatioship betwee two cotiuous variable, such as height ad weight, the cocetratio of a ijected drug ad heart rate, or the cosumptio

More information

TI-89, TI-92 Plus or Voyage 200 for Non-Business Statistics

TI-89, TI-92 Plus or Voyage 200 for Non-Business Statistics Chapter 3 TI-89, TI-9 Plu or Voyage 00 for No-Buie Statitic Eterig Data Pre [APPS], elect FlahApp the pre [ENTER]. Highlight Stat/Lit Editor the pre [ENTER]. Pre [ENTER] agai to elect the mai folder. (Note:

More information

Confidence Intervals. CI for a population mean (σ is known and n > 30 or the variable is normally distributed in the.

Confidence Intervals. CI for a population mean (σ is known and n > 30 or the variable is normally distributed in the. Cofidece Itervals A cofidece iterval is a iterval whose purpose is to estimate a parameter (a umber that could, i theory, be calculated from the populatio, if measuremets were available for the whole populatio).

More information

*The most important feature of MRP as compared with ordinary inventory control analysis is its time phasing feature.

*The most important feature of MRP as compared with ordinary inventory control analysis is its time phasing feature. Itegrated Productio ad Ivetory Cotrol System MRP ad MRP II Framework of Maufacturig System Ivetory cotrol, productio schedulig, capacity plaig ad fiacial ad busiess decisios i a productio system are iterrelated.

More information

GCSE STATISTICS. 4) How to calculate the range: The difference between the biggest number and the smallest number.

GCSE STATISTICS. 4) How to calculate the range: The difference between the biggest number and the smallest number. GCSE STATISTICS You should kow: 1) How to draw a frequecy diagram: e.g. NUMBER TALLY FREQUENCY 1 3 5 ) How to draw a bar chart, a pictogram, ad a pie chart. 3) How to use averages: a) Mea - add up all

More information

More examples for Hypothesis Testing

More examples for Hypothesis Testing More example for Hypothei Tetig Part I: Compoet 1. Null ad alterative hypothee a. The ull hypothee (H 0 ) i a tatemet that the value of a populatio parameter (mea) i equal to ome claimed value. Ex H 0:

More information

CHAPTER 3 THE TIME VALUE OF MONEY

CHAPTER 3 THE TIME VALUE OF MONEY CHAPTER 3 THE TIME VALUE OF MONEY OVERVIEW A dollar i the had today is worth more tha a dollar to be received i the future because, if you had it ow, you could ivest that dollar ad ear iterest. Of all

More information

Chapter 9: Correlation and Regression: Solutions

Chapter 9: Correlation and Regression: Solutions Chapter 9: Correlatio ad Regressio: Solutios 9.1 Correlatio I this sectio, we aim to aswer the questio: Is there a relatioship betwee A ad B? Is there a relatioship betwee the umber of emploee traiig hours

More information

CHAPTER 7: Central Limit Theorem: CLT for Averages (Means)

CHAPTER 7: Central Limit Theorem: CLT for Averages (Means) CHAPTER 7: Cetral Limit Theorem: CLT for Averages (Meas) X = the umber obtaied whe rollig oe six sided die oce. If we roll a six sided die oce, the mea of the probability distributio is X P(X = x) Simulatio:

More information

Equation of a line. Line in coordinate geometry. Slope-intercept form ( 斜 截 式 ) Intercept form ( 截 距 式 ) Point-slope form ( 點 斜 式 )

Equation of a line. Line in coordinate geometry. Slope-intercept form ( 斜 截 式 ) Intercept form ( 截 距 式 ) Point-slope form ( 點 斜 式 ) Chapter : Liear Equatios Chapter Liear Equatios Lie i coordiate geometr I Cartesia coordiate sstems ( 卡 笛 兒 坐 標 系 統 ), a lie ca be represeted b a liear equatio, i.e., a polomial with degree. But before

More information

The following example will help us understand The Sampling Distribution of the Mean. C1 C2 C3 C4 C5 50 miles 84 miles 38 miles 120 miles 48 miles

The following example will help us understand The Sampling Distribution of the Mean. C1 C2 C3 C4 C5 50 miles 84 miles 38 miles 120 miles 48 miles The followig eample will help us uderstad The Samplig Distributio of the Mea Review: The populatio is the etire collectio of all idividuals or objects of iterest The sample is the portio of the populatio

More information

Measures of Spread and Boxplots Discrete Math, Section 9.4

Measures of Spread and Boxplots Discrete Math, Section 9.4 Measures of Spread ad Boxplots Discrete Math, Sectio 9.4 We start with a example: Example 1: Comparig Mea ad Media Compute the mea ad media of each data set: S 1 = {4, 6, 8, 10, 1, 14, 16} S = {4, 7, 9,

More information

POWER ANALYSIS OF INDEPENDENCE TESTING FOR CONTINGENCY TABLES

POWER ANALYSIS OF INDEPENDENCE TESTING FOR CONTINGENCY TABLES ZESZYTY NAUKOWE AKADEMII MARYNARKI WOJENNEJ SCIENTIFIC JOURNAL OF POLISH NAVAL ACADEMY 05 (LVI) (00) Piotr Sulewki, Ryzard Motyka DOI: 0.5604/0860889X.660 POWER ANALYSIS OF INDEPENDENCE TESTING FOR CONTINGENCY

More information

Biology 171L Environment and Ecology Lab Lab 2: Descriptive Statistics, Presenting Data and Graphing Relationships

Biology 171L Environment and Ecology Lab Lab 2: Descriptive Statistics, Presenting Data and Graphing Relationships Biology 171L Eviromet ad Ecology Lab Lab : Descriptive Statistics, Presetig Data ad Graphig Relatioships Itroductio Log lists of data are ofte ot very useful for idetifyig geeral treds i the data or the

More information

Chapter 7: Confidence Interval and Sample Size

Chapter 7: Confidence Interval and Sample Size Chapter 7: Cofidece Iterval ad Sample Size Learig Objectives Upo successful completio of Chapter 7, you will be able to: Fid the cofidece iterval for the mea, proportio, ad variace. Determie the miimum

More information

INVESTMENT PERFORMANCE COUNCIL (IPC)

INVESTMENT PERFORMANCE COUNCIL (IPC) INVESTMENT PEFOMANCE COUNCIL (IPC) INVITATION TO COMMENT: Global Ivestmet Performace Stadards (GIPS ) Guidace Statemet o Calculatio Methodology The Associatio for Ivestmet Maagemet ad esearch (AIM) seeks

More information

Confidence Intervals (2) QMET103

Confidence Intervals (2) QMET103 Cofidece Iterval () QMET03 Library, Teachig ad Learig Geeral Remember: three value are ued to cotruct all cofidece iterval: Samle tatitic Z or t Stadard error of amle tatitic Deciio ad Parameter to idetify:

More information

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,

More information

A technical guide to 2014 key stage 2 to key stage 4 value added measures

A technical guide to 2014 key stage 2 to key stage 4 value added measures A technical guide to 2014 key tage 2 to key tage 4 value added meaure CONTENTS Introduction: PAGE NO. What i value added? 2 Change to value added methodology in 2014 4 Interpretation: Interpreting chool

More information

Case Study. Normal and t Distributions. Density Plot. Normal Distributions

Case Study. Normal and t Distributions. Density Plot. Normal Distributions Case Study Normal ad t Distributios Bret Halo ad Bret Larget Departmet of Statistics Uiversity of Wiscosi Madiso October 11 13, 2011 Case Study Body temperature varies withi idividuals over time (it ca

More information

PSYCHOLOGICAL STATISTICS

PSYCHOLOGICAL STATISTICS UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION B Sc. Cousellig Psychology (0 Adm.) IV SEMESTER COMPLEMENTARY COURSE PSYCHOLOGICAL STATISTICS QUESTION BANK. Iferetial statistics is the brach of statistics

More information

Z-TEST / Z-STATISTIC: used to test hypotheses about. µ when the population standard deviation is unknown

Z-TEST / Z-STATISTIC: used to test hypotheses about. µ when the population standard deviation is unknown Z-TEST / Z-STATISTIC: used to test hypotheses about µ whe the populatio stadard deviatio is kow ad populatio distributio is ormal or sample size is large T-TEST / T-STATISTIC: used to test hypotheses about

More information

I. Chi-squared Distributions

I. Chi-squared Distributions 1 M 358K Supplemet to Chapter 23: CHI-SQUARED DISTRIBUTIONS, T-DISTRIBUTIONS, AND DEGREES OF FREEDOM To uderstad t-distributios, we first eed to look at aother family of distributios, the chi-squared distributios.

More information

9.8: THE POWER OF A TEST

9.8: THE POWER OF A TEST 9.8: The Power of a Test CD9-1 9.8: THE POWER OF A TEST I the iitial discussio of statistical hypothesis testig, the two types of risks that are take whe decisios are made about populatio parameters based

More information

HCL Dynamic Spiking Protocol

HCL Dynamic Spiking Protocol ELI LILLY AND COMPANY TIPPECANOE LABORATORIES LAFAYETTE, IN Revisio 2.0 TABLE OF CONTENTS REVISION HISTORY... 2. REVISION.0... 2.2 REVISION 2.0... 2 2 OVERVIEW... 3 3 DEFINITIONS... 5 4 EQUIPMENT... 7

More information

MEI Structured Mathematics. Module Summary Sheets. Statistics 2 (Version B: reference to new book)

MEI Structured Mathematics. Module Summary Sheets. Statistics 2 (Version B: reference to new book) MEI Mathematics i Educatio ad Idustry MEI Structured Mathematics Module Summary Sheets Statistics (Versio B: referece to ew book) Topic : The Poisso Distributio Topic : The Normal Distributio Topic 3:

More information

5: Introduction to Estimation

5: Introduction to Estimation 5: Itroductio to Estimatio Cotets Acroyms ad symbols... 1 Statistical iferece... Estimatig µ with cofidece... 3 Samplig distributio of the mea... 3 Cofidece Iterval for μ whe σ is kow before had... 4 Sample

More information

7. Sample Covariance and Correlation

7. Sample Covariance and Correlation 1 of 8 7/16/2009 6:06 AM Virtual Laboratories > 6. Radom Samples > 1 2 3 4 5 6 7 7. Sample Covariace ad Correlatio The Bivariate Model Suppose agai that we have a basic radom experimet, ad that X ad Y

More information

Center, Spread, and Shape in Inference: Claims, Caveats, and Insights

Center, Spread, and Shape in Inference: Claims, Caveats, and Insights Ceter, Spread, ad Shape i Iferece: Claims, Caveats, ad Isights Dr. Nacy Pfeig (Uiversity of Pittsburgh) AMATYC November 2008 Prelimiary Activities 1. I would like to produce a iterval estimate for the

More information

The second difference is the sequence of differences of the first difference sequence, 2

The second difference is the sequence of differences of the first difference sequence, 2 Differece Equatios I differetial equatios, you look for a fuctio that satisfies ad equatio ivolvig derivatives. I differece equatios, istead of a fuctio of a cotiuous variable (such as time), we look for

More information

THE ARITHMETIC OF INTEGERS. - multiplication, exponentiation, division, addition, and subtraction

THE ARITHMETIC OF INTEGERS. - multiplication, exponentiation, division, addition, and subtraction THE ARITHMETIC OF INTEGERS - multiplicatio, expoetiatio, divisio, additio, ad subtractio What to do ad what ot to do. THE INTEGERS Recall that a iteger is oe of the whole umbers, which may be either positive,

More information

4.1 Sigma Notation and Riemann Sums

4.1 Sigma Notation and Riemann Sums 0 the itegral. Sigma Notatio ad Riema Sums Oe strategy for calculatig the area of a regio is to cut the regio ito simple shapes, calculate the area of each simple shape, ad the add these smaller areas

More information

Descriptive Statistics

Descriptive Statistics Descriptive Statistics We leared to describe data sets graphically. We ca also describe a data set umerically. Measures of Locatio Defiitio The sample mea is the arithmetic average of values. We deote

More information

Basic Elements of Arithmetic Sequences and Series

Basic Elements of Arithmetic Sequences and Series MA40S PRE-CALCULUS UNIT G GEOMETRIC SEQUENCES CLASS NOTES (COMPLETED NO NEED TO COPY NOTES FROM OVERHEAD) Basic Elemets of Arithmetic Sequeces ad Series Objective: To establish basic elemets of arithmetic

More information

France caters to innovative companies and offers the best research tax credit in Europe

France caters to innovative companies and offers the best research tax credit in Europe 1/5 The Frech Govermet has three objectives : > improve Frace s fiscal competitiveess > cosolidate R&D activities > make Frace a attractive coutry for iovatio Tax icetives have become a key elemet of public

More information

THE PRINCIPLE OF THE ACTIVE JMC SCATTERER. Seppo Uosukainen

THE PRINCIPLE OF THE ACTIVE JMC SCATTERER. Seppo Uosukainen THE PRINCIPLE OF THE ACTIVE JC SCATTERER Seppo Uoukaie VTT Buildig ad Tapot Ai Hadlig Techology ad Acoutic P. O. Bo 1803, FIN 02044 VTT, Filad Seppo.Uoukaie@vtt.fi ABSTRACT The piciple of fomulatig the

More information

Overview. Learning Objectives. Point Estimate. Estimation. Estimating the Value of a Parameter Using Confidence Intervals

Overview. Learning Objectives. Point Estimate. Estimation. Estimating the Value of a Parameter Using Confidence Intervals Overview Estimatig the Value of a Parameter Usig Cofidece Itervals We apply the results about the sample mea the problem of estimatio Estimatio is the process of usig sample data estimate the value of

More information

Vladimir N. Burkov, Dmitri A. Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT

Vladimir N. Burkov, Dmitri A. Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT Keywords: project maagemet, resource allocatio, etwork plaig Vladimir N Burkov, Dmitri A Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT The paper deals with the problems of resource allocatio betwee

More information

Gregory Carey, 1998 Linear Transformations & Composites - 1. Linear Transformations and Linear Composites

Gregory Carey, 1998 Linear Transformations & Composites - 1. Linear Transformations and Linear Composites Gregory Carey, 1998 Liear Trasformatios & Composites - 1 Liear Trasformatios ad Liear Composites I Liear Trasformatios of Variables Meas ad Stadard Deviatios of Liear Trasformatios A liear trasformatio

More information

3. If x and y are real numbers, what is the simplified radical form

3. If x and y are real numbers, what is the simplified radical form lgebra II Practice Test Objective:.a. Which is equivalet to 98 94 4 49?. Which epressio is aother way to write 5 4? 5 5 4 4 4 5 4 5. If ad y are real umbers, what is the simplified radical form of 5 y

More information

Unit 11 Using Linear Regression to Describe Relationships

Unit 11 Using Linear Regression to Describe Relationships Unit 11 Uing Linear Regreion to Decribe Relationhip Objective: To obtain and interpret the lope and intercept of the leat quare line for predicting a quantitative repone variable from a quantitative explanatory

More information

Key Ideas Section 8-1: Overview hypothesis testing Hypothesis Hypothesis Test Section 8-2: Basics of Hypothesis Testing Null Hypothesis

Key Ideas Section 8-1: Overview hypothesis testing Hypothesis Hypothesis Test Section 8-2: Basics of Hypothesis Testing Null Hypothesis Chapter 8 Key Ideas Hypothesis (Null ad Alterative), Hypothesis Test, Test Statistic, P-value Type I Error, Type II Error, Sigificace Level, Power Sectio 8-1: Overview Cofidece Itervals (Chapter 7) are

More information

Domain 1: Designing a SQL Server Instance and a Database Solution

Domain 1: Designing a SQL Server Instance and a Database Solution Maual SQL Server 2008 Desig, Optimize ad Maitai (70-450) 1-800-418-6789 Domai 1: Desigig a SQL Server Istace ad a Database Solutio Desigig for CPU, Memory ad Storage Capacity Requiremets Whe desigig a

More information

NATIONAL SENIOR CERTIFICATE GRADE 12

NATIONAL SENIOR CERTIFICATE GRADE 12 NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P EXEMPLAR 04 MARKS: 50 TIME: 3 hours This questio paper cosists of 8 pages ad iformatio sheet. Please tur over Mathematics/P DBE/04 NSC Grade Eemplar INSTRUCTIONS

More information

Subject CT5 Contingencies Core Technical Syllabus

Subject CT5 Contingencies Core Technical Syllabus Subject CT5 Cotigecies Core Techical Syllabus for the 2015 exams 1 Jue 2014 Aim The aim of the Cotigecies subject is to provide a groudig i the mathematical techiques which ca be used to model ad value

More information

Measures of Central Tendency

Measures of Central Tendency Measures of Cetral Tedecy A studet s grade will be determied by exam grades ( each exam couts twice ad there are three exams, HW average (couts oce, fial exam ( couts three times. Fid the average if the

More information

Analyzing Longitudinal Data from Complex Surveys Using SUDAAN

Analyzing Longitudinal Data from Complex Surveys Using SUDAAN Aalyzig Logitudial Data from Complex Surveys Usig SUDAAN Darryl Creel Statistics ad Epidemiology, RTI Iteratioal, 312 Trotter Farm Drive, Rockville, MD, 20850 Abstract SUDAAN: Software for the Statistical

More information

THE REGRESSION MODEL IN MATRIX FORM. For simple linear regression, meaning one predictor, the model is. for i = 1, 2, 3,, n

THE REGRESSION MODEL IN MATRIX FORM. For simple linear regression, meaning one predictor, the model is. for i = 1, 2, 3,, n We will cosider the liear regressio model i matrix form. For simple liear regressio, meaig oe predictor, the model is i = + x i + ε i for i =,,,, This model icludes the assumptio that the ε i s are a sample

More information

HANDOUT E.17 - EXAMPLES ON BODE PLOTS OF FIRST AND SECOND ORDER SYSTEMS

HANDOUT E.17 - EXAMPLES ON BODE PLOTS OF FIRST AND SECOND ORDER SYSTEMS Lecture 7,8 Augut 8, 00 HANDOUT E7 - EXAMPLES ON BODE PLOTS OF FIRST AND SECOND ORDER SYSTEMS Example Obtai the Bode plot of the ytem give by the trafer fuctio ( We covert the trafer fuctio i the followig

More information

Definition. A variable X that takes on values X 1, X 2, X 3,...X k with respective frequencies f 1, f 2, f 3,...f k has mean

Definition. A variable X that takes on values X 1, X 2, X 3,...X k with respective frequencies f 1, f 2, f 3,...f k has mean 1 Social Studies 201 October 13, 2004 Note: The examples i these otes may be differet tha used i class. However, the examples are similar ad the methods used are idetical to what was preseted i class.

More information

Modified Line Search Method for Global Optimization

Modified Line Search Method for Global Optimization Modified Lie Search Method for Global Optimizatio Cria Grosa ad Ajith Abraham Ceter of Excellece for Quatifiable Quality of Service Norwegia Uiversity of Sciece ad Techology Trodheim, Norway {cria, ajith}@q2s.tu.o

More information

On k-connectivity and Minimum Vertex Degree in Random s-intersection Graphs

On k-connectivity and Minimum Vertex Degree in Random s-intersection Graphs O k-coectivity ad Miimum Vertex Degree i Radom -Iterectio Graph Ju Zhao Oma Yağa Virgil Gligor CyLab ad Dept. of ECE Caregie Mello Uiverity Email: {juzhao, oyaga, virgil}@adrew.cmu.edu Abtract Radom -iterectio

More information

Hypothesis testing. Null and alternative hypotheses

Hypothesis testing. Null and alternative hypotheses Hypothesis testig Aother importat use of samplig distributios is to test hypotheses about populatio parameters, e.g. mea, proportio, regressio coefficiets, etc. For example, it is possible to stipulate

More information

Chair for Network Architectures and Services Institute of Informatics TU München Prof. Carle. Network Security. Chapter 2 Basics

Chair for Network Architectures and Services Institute of Informatics TU München Prof. Carle. Network Security. Chapter 2 Basics Chair for Network Architectures ad Services Istitute of Iformatics TU Müche Prof. Carle Network Security Chapter 2 Basics 2.4 Radom Number Geeratio for Cryptographic Protocols Motivatio It is crucial to

More information

Engineering 323 Beautiful Homework Set 3 1 of 7 Kuszmar Problem 2.51

Engineering 323 Beautiful Homework Set 3 1 of 7 Kuszmar Problem 2.51 Egieerig 33 eautiful Homewor et 3 of 7 Kuszmar roblem.5.5 large departmet store sells sport shirts i three sizes small, medium, ad large, three patters plaid, prit, ad stripe, ad two sleeve legths log

More information

Research Method (I) --Knowledge on Sampling (Simple Random Sampling)

Research Method (I) --Knowledge on Sampling (Simple Random Sampling) Research Method (I) --Kowledge o Samplig (Simple Radom Samplig) 1. Itroductio to samplig 1.1 Defiitio of samplig Samplig ca be defied as selectig part of the elemets i a populatio. It results i the fact

More information

ISO tadard o determiatio of the Detectio Limit ad Deciio threhod for ioiig radiatio meauremet ISO/CD 1199-1: Determiatio of the Detectio Limit ad Deci

ISO tadard o determiatio of the Detectio Limit ad Deciio threhod for ioiig radiatio meauremet ISO/CD 1199-1: Determiatio of the Detectio Limit ad Deci ICRM Gamma Spectrometry Workig Group Workhop Pari, Laoratoire atioa d Eai 3-4 Feruary 9 Detectio imit Deciio threhod Appicatio of ISO 1199 P. De Feice EEA atioa Ititute for Ioiig Radiatio Metroogy defeice@caaccia.eea.it.1/13

More information

Lesson 17 Pearson s Correlation Coefficient

Lesson 17 Pearson s Correlation Coefficient Outlie Measures of Relatioships Pearso s Correlatio Coefficiet (r) -types of data -scatter plots -measure of directio -measure of stregth Computatio -covariatio of X ad Y -uique variatio i X ad Y -measurig

More information

CS103X: Discrete Structures Homework 4 Solutions

CS103X: Discrete Structures Homework 4 Solutions CS103X: Discrete Structures Homewor 4 Solutios Due February 22, 2008 Exercise 1 10 poits. Silico Valley questios: a How may possible six-figure salaries i whole dollar amouts are there that cotai at least

More information

3D BUILDING MODEL RECONSTRUCTION FROM POINT CLOUDS AND GROUND PLANS

3D BUILDING MODEL RECONSTRUCTION FROM POINT CLOUDS AND GROUND PLANS 3D BUILDING MODEL RECONSTRUCTION FROM POINT CLOUDS AND GROUND PLANS George Voelma ad Sader Dijkma Departmet of Geodey Delft Uiverity of Techology The Netherlad g.voelma@geo.tudelft.l KEY WORDS: Buildig

More information

3.1 Measures of Central Tendency. Introduction 5/28/2013. Data Description. Outline. Objectives. Objectives. Traditional Statistics Average

3.1 Measures of Central Tendency. Introduction 5/28/2013. Data Description. Outline. Objectives. Objectives. Traditional Statistics Average 5/8/013 C H 3A P T E R Outlie 3 1 Measures of Cetral Tedecy 3 Measures of Variatio 3 3 3 Measuresof Positio 3 4 Exploratory Data Aalysis Copyright 013 The McGraw Hill Compaies, Ic. C H 3A P T E R Objectives

More information

Non-life insurance mathematics. Nils F. Haavardsson, University of Oslo and DNB Skadeforsikring

Non-life insurance mathematics. Nils F. Haavardsson, University of Oslo and DNB Skadeforsikring No-life isurace mathematics Nils F. Haavardsso, Uiversity of Oslo ad DNB Skadeforsikrig Mai issues so far Why does isurace work? How is risk premium defied ad why is it importat? How ca claim frequecy

More information

The analysis of the Cournot oligopoly model considering the subjective motive in the strategy selection

The analysis of the Cournot oligopoly model considering the subjective motive in the strategy selection The aalysis of the Courot oligopoly model cosiderig the subjective motive i the strategy selectio Shigehito Furuyama Teruhisa Nakai Departmet of Systems Maagemet Egieerig Faculty of Egieerig Kasai Uiversity

More information

A probabilistic proof of a binomial identity

A probabilistic proof of a binomial identity A probabilistic proof of a biomial idetity Joatho Peterso Abstract We give a elemetary probabilistic proof of a biomial idetity. The proof is obtaied by computig the probability of a certai evet i two

More information

The Wider Role and Benefits of Investors in People

The Wider Role and Benefits of Investors in People RESEARCH The Wider Role ad Beefit of Ivetor i People Mark Cox ad Rod Spire PACEC Reearch Report RR360 Reearch Report No 360 The Wider Role ad Beefit of Ivetor i People Mark Cox ad Rod Spire PACEC The view

More information

CS103A Handout 23 Winter 2002 February 22, 2002 Solving Recurrence Relations

CS103A Handout 23 Winter 2002 February 22, 2002 Solving Recurrence Relations CS3A Hadout 3 Witer 00 February, 00 Solvig Recurrece Relatios Itroductio A wide variety of recurrece problems occur i models. Some of these recurrece relatios ca be solved usig iteratio or some other ad

More information

Annuities Under Random Rates of Interest II By Abraham Zaks. Technion I.I.T. Haifa ISRAEL and Haifa University Haifa ISRAEL.

Annuities Under Random Rates of Interest II By Abraham Zaks. Technion I.I.T. Haifa ISRAEL and Haifa University Haifa ISRAEL. Auities Uder Radom Rates of Iterest II By Abraham Zas Techio I.I.T. Haifa ISRAEL ad Haifa Uiversity Haifa ISRAEL Departmet of Mathematics, Techio - Israel Istitute of Techology, 3000, Haifa, Israel I memory

More information

Chapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions

Chapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions Chapter 5 Uit Aual Amout ad Gradiet Fuctios IET 350 Egieerig Ecoomics Learig Objectives Chapter 5 Upo completio of this chapter you should uderstad: Calculatig future values from aual amouts. Calculatig

More information

Lesson 15 ANOVA (analysis of variance)

Lesson 15 ANOVA (analysis of variance) Outlie Variability -betwee group variability -withi group variability -total variability -F-ratio Computatio -sums of squares (betwee/withi/total -degrees of freedom (betwee/withi/total -mea square (betwee/withi

More information

Sampling Distribution And Central Limit Theorem

Sampling Distribution And Central Limit Theorem () Samplig Distributio & Cetral Limit Samplig Distributio Ad Cetral Limit Samplig distributio of the sample mea If we sample a umber of samples (say k samples where k is very large umber) each of size,

More information

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008 I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces

More information

Trigonometric Form of a Complex Number. The Complex Plane. axis. ( 2, 1) or 2 i FIGURE 6.44. The absolute value of the complex number z a bi is

Trigonometric Form of a Complex Number. The Complex Plane. axis. ( 2, 1) or 2 i FIGURE 6.44. The absolute value of the complex number z a bi is 0_0605.qxd /5/05 0:45 AM Page 470 470 Chapter 6 Additioal Topics i Trigoometry 6.5 Trigoometric Form of a Complex Number What you should lear Plot complex umbers i the complex plae ad fid absolute values

More information

3. Covariance and Correlation

3. Covariance and Correlation Virtual Laboratories > 3. Expected Value > 1 2 3 4 5 6 3. Covariace ad Correlatio Recall that by takig the expected value of various trasformatios of a radom variable, we ca measure may iterestig characteristics

More information

where: T = number of years of cash flow in investment's life n = the year in which the cash flow X n i = IRR = the internal rate of return

where: T = number of years of cash flow in investment's life n = the year in which the cash flow X n i = IRR = the internal rate of return EVALUATING ALTERNATIVE CAPITAL INVESTMENT PROGRAMS By Ke D. Duft, Extesio Ecoomist I the March 98 issue of this publicatio we reviewed the procedure by which a capital ivestmet project was assessed. The

More information

A Resource for Free-standing Mathematics Qualifications Working with %

A Resource for Free-standing Mathematics Qualifications Working with % Ca you aswer these questios? A savigs accout gives % iterest per aum.. If 000 is ivested i this accout, how much will be i the accout at the ed of years? A ew car costs 16 000 ad its value falls by 1%

More information

Output Analysis (2, Chapters 10 &11 Law)

Output Analysis (2, Chapters 10 &11 Law) B. Maddah ENMG 6 Simulatio 05/0/07 Output Aalysis (, Chapters 10 &11 Law) Comparig alterative system cofiguratio Sice the output of a simulatio is radom, the comparig differet systems via simulatio should

More information

Chapter XIV: Fundamentals of Probability and Statistics *

Chapter XIV: Fundamentals of Probability and Statistics * Objectives Chapter XIV: Fudametals o Probability ad Statistics * Preset udametal cocepts o probability ad statistics Review measures o cetral tedecy ad dispersio Aalyze methods ad applicatios o descriptive

More information

1 Computing the Standard Deviation of Sample Means

1 Computing the Standard Deviation of Sample Means Computig the Stadard Deviatio of Sample Meas Quality cotrol charts are based o sample meas ot o idividual values withi a sample. A sample is a group of items, which are cosidered all together for our aalysis.

More information

TIME SERIES ANALYSIS AND TRENDS BY USING SPSS PROGRAMME

TIME SERIES ANALYSIS AND TRENDS BY USING SPSS PROGRAMME TIME SERIES ANALYSIS AND TRENDS BY USING SPSS PROGRAMME RADMILA KOCURKOVÁ Sileian Univerity in Opava School of Buine Adminitration in Karviná Department of Mathematical Method in Economic Czech Republic

More information

0.7 0.6 0.2 0 0 96 96.5 97 97.5 98 98.5 99 99.5 100 100.5 96.5 97 97.5 98 98.5 99 99.5 100 100.5

0.7 0.6 0.2 0 0 96 96.5 97 97.5 98 98.5 99 99.5 100 100.5 96.5 97 97.5 98 98.5 99 99.5 100 100.5 Sectio 13 Kolmogorov-Smirov test. Suppose that we have a i.i.d. sample X 1,..., X with some ukow distributio P ad we would like to test the hypothesis that P is equal to a particular distributio P 0, i.e.

More information

Chapter 10 Student Lecture Notes 10-1

Chapter 10 Student Lecture Notes 10-1 Chapter 0 tudet Lecture Notes 0- Basic Busiess tatistics (9 th Editio) Chapter 0 Two-ample Tests with Numerical Data 004 Pretice-Hall, Ic. Chap 0- Chapter Topics Comparig Two Idepedet amples Z test for

More information

ODBC. Getting Started With Sage Timberline Office ODBC

ODBC. Getting Started With Sage Timberline Office ODBC ODBC Gettig Started With Sage Timberlie Office ODBC NOTICE This documet ad the Sage Timberlie Office software may be used oly i accordace with the accompayig Sage Timberlie Office Ed User Licese Agreemet.

More information

Quadrat Sampling in Population Ecology

Quadrat Sampling in Population Ecology Quadrat Samplig i Populatio Ecology Backgroud Estimatig the abudace of orgaisms. Ecology is ofte referred to as the "study of distributio ad abudace". This beig true, we would ofte like to kow how may

More information

Uncertainty Chapter 13. Mausam (Based on slides by UW-AI faculty)

Uncertainty Chapter 13. Mausam (Based on slides by UW-AI faculty) Ucertait Chapter 3 Mausam Based o slides b UW-AI facult Kowledge Represetatio KR Laguage Otological Commitmet Epistemological Commitmet ropositioal Logic facts true false ukow First Order Logic facts objects

More information

An Overview of Experimental Design

An Overview of Experimental Design A Overview of Experimetal Deig I. Hypothei Tetig While much reearch i Biology coit of data collectio for decriptive purpoe, there i a burgeoig tred toward collectig iformatio with the hope of awerig particular

More information

FM4 CREDIT AND BORROWING

FM4 CREDIT AND BORROWING FM4 CREDIT AND BORROWING Whe you purchase big ticket items such as cars, boats, televisios ad the like, retailers ad fiacial istitutios have various terms ad coditios that are implemeted for the cosumer

More information

Mann-Whitney U 2 Sample Test (a.k.a. Wilcoxon Rank Sum Test)

Mann-Whitney U 2 Sample Test (a.k.a. Wilcoxon Rank Sum Test) No-Parametric ivariate Statistics: Wilcoxo-Ma-Whitey 2 Sample Test 1 Ma-Whitey 2 Sample Test (a.k.a. Wilcoxo Rak Sum Test) The (Wilcoxo-) Ma-Whitey (WMW) test is the o-parametric equivalet of a pooled

More information

THE MLS ANALYSIS TECHNIQUE AND CLIO

THE MLS ANALYSIS TECHNIQUE AND CLIO THE MLS ANALYSIS TECHNIQUE AND CLIO CONTENTS Itroductio... MLS Sequece... Te cro-correlatio...3 Example... Bibliograpy...5 Rev.0-9 Dec 997 Itroductio Te MLS aalyi aim to caracterize te beaviour of te ytem

More information

Factoring x n 1: cyclotomic and Aurifeuillian polynomials Paul Garrett

Factoring x n 1: cyclotomic and Aurifeuillian polynomials Paul Garrett <garrett@math.umn.edu> (March 16, 004) Factorig x 1: cyclotomic ad Aurifeuillia polyomials Paul Garrett Polyomials of the form x 1, x 3 1, x 4 1 have at least oe systematic factorizatio x 1 = (x 1)(x 1

More information

Soving Recurrence Relations

Soving Recurrence Relations Sovig Recurrece Relatios Part 1. Homogeeous liear 2d degree relatios with costat coefficiets. Cosider the recurrece relatio ( ) T () + at ( 1) + bt ( 2) = 0 This is called a homogeeous liear 2d degree

More information

Forecasting. Forecasting Application. Practical Forecasting. Chapter 7 OVERVIEW KEY CONCEPTS. Chapter 7. Chapter 7

Forecasting. Forecasting Application. Practical Forecasting. Chapter 7 OVERVIEW KEY CONCEPTS. Chapter 7. Chapter 7 Forecastig Chapter 7 Chapter 7 OVERVIEW Forecastig Applicatios Qualitative Aalysis Tred Aalysis ad Projectio Busiess Cycle Expoetial Smoothig Ecoometric Forecastig Judgig Forecast Reliability Choosig the

More information

Review for 1 sample CI Name. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Review for 1 sample CI Name. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Review for 1 sample CI Name MULTIPLE CHOICE. Choose the oe alterative that best completes the statemet or aswers the questio. Fid the margi of error for the give cofidece iterval. 1) A survey foud that

More information

Systems Design Project: Indoor Location of Wireless Devices

Systems Design Project: Indoor Location of Wireless Devices Systems Desig Project: Idoor Locatio of Wireless Devices Prepared By: Bria Murphy Seior Systems Sciece ad Egieerig Washigto Uiversity i St. Louis Phoe: (805) 698-5295 Email: bcm1@cec.wustl.edu Supervised

More information