
jaid-pareekshan

 
aeye "jaid"-pareekshan koee bhee saankhyikiya pareekshan haye jisake liye shoonya parikalpana key tahat pareekshan saankhyiki key vitaran koo ack samanya vitaran dwara anumaanit kiya jaa sakata haye. jaid-pareekshan vitaran key maadhya kaa pareekshan karate hain. aatmavishvaas antaral mein pratyek mahatva star key liye, "jaid"-pareekshan kaa ack hii mahatvapurna moolya hotaa haye (udaaharan key liye, 5 pratishat dou poonchh vaale key liye 1.96) joe ise chhaatr key "tii"-pareekshan kii tulanaa mein adhik suvidhajanak banaata haye, jisake mahatvapurna moolyon koo namuna aakar (swatantrata kii sambandhit degree key madhyam seey) dwara paribhaashit kiya jaataa haye. jaid-test aur chhaatr key tii-test donon mein samaantaa haye kii way donon detta key ack samooh key mahatva koo nirdhaarit karane mein madad karate hain. haalaanki, jaid-pareekshan kaa upayog vyavhaar mein shayed hii kabhi kiya jaataa haye kyonki jansankhya vichalan kaa nirdhaaran karna mushkil haye.
upayuktata.
kendriya seema pramey key kaaran, kaee pareekshan aankade lagbhag aam taur parr badey namoonon key liye vitarit kiye jaate hain. isaliye, kaee saankhyikiya parikshanon koo aasaani seey anumaanit "jaid"-parikshanon key roop mein kiya jaa sakata haye yadi namuna aakar badaa haye yaa jansankhya bhinnata gyaat haye. yadi jansankhya bhinnata agyaat haye (aur isaliye namoone seey hii anuman lagaaya jaanaa haye) aur namuna aakar badaa naheen haye ("aine" <30), tou chhaatr kaa "tii"-pareekshan adhik upayukt hoe sakata haye (kuchh mamalon mein, "aine" <50, jaisa kii neeche varnit haye).
prakriya.
jaba "tii" ack aankada haye joe lagbhag samanya roop seey null parikalpana key tahat vitarit kiya jaataa haye tou jaid pareekshan kaise kiya jaaeh 
sabse pahale, shoonya parikalpana key tahat "t" key apekshit moolya kaa anuman lagaaen, aur "t" key maanak vichalan kaa anuman "s" praapt karein.
doosara, "tii" key gunon kaa nirdhaaran karenh ack poonchh yaa dou poonchh.
null parikalpana key liye h "0: μ ≤ μ" 0 banaam vaikalpik parikalpana h "1: μ <μ" 0, yeh nichali/baain-poonchh (ack poonchh) haye.
null parikalpana key liye h "0: μ ≤ μ" 0 banaam vaikalpik parikalpana h "1: μ> μ" 0, yeh oopari/daaeen-poonchh (ack poonchh) haye. 
null parikalpana key liye h "0: μ = μ" 0 banaam vaikalpik parikalpana h "1: μ ≤ μ" 0, yeh dou-poonchh vaalaa haye. 
teesara, maanak ank kii ganana keejiyeh sootra _ 1 jise ack-poonchh aur dou-poonchh vaale "p"-maanon kii ganana φ ("z") (nichali/baain-poonchh vaale parikshanon key liye), φ (− "z") (oopari/daaeen-poonchh vaale parikshanon key liye) aur 2φ (−) key roop mein kii jaa sakati haye.."jaid".) (dou-poonchh vaale parikshanon key liye) jahan φ maanak samanya sanchayi vitaran kaary haye.
shartein.
jaid"-pareekshan lagu honey key liye, kuchh sharton koo puuraa karna hoga.
yadi oopar charcha kiye gaye upadrav maapdandon key anumaanon koo jodaa gayaa haye, tou detta key namoone lene key tareeke key liye upayukt anumaanon kaa upayog karna mahatvapurna haye. ack yaa dou namuna sthaan samasya key liye "jaid"-parikshanon key vishesh mamle mein, samanya namuna maanak vichalan kewal tabhi upayukt haye jaba detta koo ack swatantra namoone key roop mein ekatra kiya gayaa hoe.
kuchh sthitiyon mein, ack aisaa pareekshan taiyar karna sambhav haye joe upadrav maapdandon key plug-inn anumaanon mein bhinnata key liye thheek seey jimmedaar hoe. ack aur dou namuna sthaan samasyaon key mamle mein, ack "tii"-pareekshan aisaa kartaa haye.
udaaharan lein.
maan leejiye kii kissy vishesh bhaugolik kshetra mein, ack pathan pareekshan parr ankon kaa ausat aur maanak vichalan kramshah 100 ank aur 12 ank haye. hamari ruchi kissy vishesh vidyalaya mein 55 chhatron key ankon mein haye, jinhone 96 kaa ausat ank praapt kiya haye. humm poochh sakate hain kii kyaa yeh ausat ank kshetriya ausat seey kaafee cumm haye-yaani, kyaa iss vidyalaya key chhaatr poore kshetra key 55 chhatron key ack sadharan yaadrichhik namoone seey tulaniya hain, yaa kyaa unake ank aashcharyajanak roop seey cumm hain?
pahale maadhya kii maanak truti kii ganana keejiyeh
jahan sootra _ 6 jansankhya maanak vichalan haye.
isake baad "z"-ank kii ganana karein, joe maanak truti kii ikaaiyon mein namuna maadhya seey jansankhya maadhya taka kii doori haih
iss udaaharan mein, humm jansankhya key ausat aur bhinnata koo gyaat maanate hain, joe kii upayukt hoga yadi kshetra key sabhi chhatron kaa pareekshan kiya jaae. jaba jansankhya key mapdand agyaat houn, tou isake bajaay ack chhaatr kaa tii-test aayojit kiya jaanaa chaahiye.
kaksha kaa ausat ank 96 haye, joe 100 kii jansankhya key ausat seey-2.47 maanak truti ikaaiyaan hain. maanak samanya vitaran sanchayi sambhavana kii ack talika mein "z"-ank koo dekhate hue, humm paate hain kii-2.47 seey neeche ack maanak samanya moolya koo dekhane kii sambhavana lagbhag 0.5 − 0.4932 = 0.0068 haye. yeh shoonya parikalpana key liye ektarafa "p"-maan haye kii 55 chhaatr sabhi pareekshan lene vaalon kii aabaadi seey ack saral yaadrichhik namoone key saath tulaniya hain. dou-pakshiya "pee"-maan lagbhag 0.014 (ektarafa "pee"-maan seey doguna) haye.
cheejon koo bataane kaa ack aur tarika yeh haye kii sambhavana 1 − 0.014 = 0.986 key saath, 55 chhatron key ack sadharan yaadrichhik namoone mein jansankhya ausat kii 4 ikaaiyon key bheetar ack ausat pareekshan ank hoga. humm yeh bhee kaha sakate hain kii 98.6% vishvaas key saath humm iss shoonya parikalpana koo aswikar karate hain kii 55 pareekshan lene vaale pareekshan lene vaalon kii aabaadi key ack sadharan yaadrichhik namoone key saath tulaniya hain.
jaid"-pareekshan hamein bataata haye kii ruchi rakhane vaale 55 chhatron kaa ausat pareekshan score asamanya roop seey cumm haye, jabaki pareekshan lene vaalon kii aabaadi mein samaan aakar key sabse saral yaadrichhik namoonon kii tulanaa mein. iss vishleshan kii kamee yeh haye kii yeh iss baat parr vichaar naheen kartaa haye kii kyaa 4 ankon kaa prabhaav aakar saarthak haye. yadi humm ack kaksha key bajaay, 900 chhatron vaale ack upa-kshetra parr vichaar karate hain, jinake ausat ank 99 they, tou lagbhag samaan "jaid"-score aur "pee"-maan dekhaa jaayega. isase pataa chalata haye kii yadi namuna kaa aakar kaafee badaa haye, tou shoonya moolya seey bahut chhote antar saankhyikiya roop seey atyadhik mahatvapurna hoe sakate hain. iss mudde parr aage kii charcha key liye saankhyikiya parikalpana pareekshan dekhein.
"jaid"-sthaan parikshanon key alawa anya pareekshan.
sthaan pareekshan sabse parichit "jaid"-pareekshan hain. jaid"-parikshanon kaa ack anya varg ack parametric saankhyikiya model mein maapdandon key adhikatam sambhavana anuman mein utpann hotaa haye. kuchh sthitiyon mein adhikatam sambhavana anuman lagbhag samanya hain, aur unake asymptotic bhinnata kii ganana machuaaron kii jaankaari key sandarbh mein kii jaa sakati haye. isaki maanak truti dwara vibhajit adhikatam sambhavana anuman kaa upayog shoonya parikalpana key liye ack pareekshan saankhyiki key roop mein kiya jaa sakata haye kii parameter kaa jansankhya moolya shoonya key barabar haye. adhik aam taur parr, yadi sootra _ 8 ack parameter θ kaa adhikatam sambhavana anuman haye, aur θ0 null parikalpana key tahat θ kaa moolya haye,

