Mahuʻinga Fakasitetisitika
Ko e “mahuʻinga” ʻoku ʻuhinga ia ki he meʻa ʻoku ʻikai ngalingali ke hoko ʻi ha veʻeteka faitotonu, ʻo ʻikai ko e “moʻoni” pea ʻikai ko e “tupu”.
Ko ha mahuʻinga p ʻo e 0.05 ʻoku ʻuhinga ia ʻe ʻomi ʻe ha veʻeteka faitotonu ha fōtunga ʻoku taʻetatau pehē ʻo tuʻo taha ʻi he uofulu. Kapau te ke vakaiʻi ha veʻeteka ʻe uofulu, ʻe paasi ha taha ʻi he meʻa hoko noa pē.
Ko e hā ʻa e mahuʻinga p
Ko e ngalingalimatematikaNgalingaliKo e faingamālie ʻo ha ola, mei he 0 ki he 1 pe 0% ki he 100%. Fika ʻe taha: 1/37 = 2.70%.Lau kotoa → ke sio ki ha mavahe ʻoku lahi tatau pe lahi ange ʻi he meʻa naʻe sio ki ai, kapau naʻe faitotonu ʻa e veʻeteka. Ko ha fakamatala ia ki he ngaahi fakamatala ʻi ha fakakaukau ʻoku tali, ʻo ʻikai ki he veʻeteka. Ko ha mahuʻinga plēpiMahuʻinga pKo e ngalingali ke sio ki ha mavahe ʻoku lahi tatau pe lahi ange ʻi he meʻa naʻe sio ki ai kapau naʻe faitotonu ʻa e veʻeteka.Lau kotoa → ʻo e 0.03 ʻoku ne pehē: ʻoku fai eni ʻe ha veʻeteka faitotonu ʻi he 3% ʻo e taimi. ʻOku ʻikai te ne pehē: ʻoku ʻi ai ha faingamālie ʻo e 97% ʻoku hehema ʻa e veʻeteka. Ko e fakamatala hono ua ʻe fie maʻu ai ke ʻiloʻi pe ʻoku angamaheni fēfē ʻa e ngaahi veʻeteka hehemalēpiVeʻeteka hehemaKo ha veʻeteka ʻoku ʻi ai hano ngaahi maumau fakatuʻasino ʻoku ne ʻai ke ngalingali lahi ange ʻa e ngaahi luo ʻe niʻihi ʻi he 1/37. ʻOku tātāitaha, pea ʻoku ʻiloʻi pē ʻaki ha ngaahi afe ʻo e ngaahi vilo kuo hiki.Lau kotoa → mei he kamataʻanga, pea ʻi ha kasino ʻo onopooni ʻoku tātātaha ʻaupito ia, ʻa ia ʻoku ngalingali lahi ange ai ko ha ola mahuʻinga pē ʻe taha ko ha meʻa hoko noa pē ʻi ha meʻa moʻoni kuo ʻilo.
Ngaahi fakahoa lahi
Ko e sivi kotoa pē ʻoku ke fai ʻi ha veʻeteka faitotonu ʻoku ʻi ai hono faingamālie ʻo e 5% ke paasi ʻi he tuʻunga ʻo e 5%. Siviʻi ha veʻeteka ʻe uofulu pea ʻe paasi ha taha. Siviʻi ha veʻeteka ʻe taha ʻi ha vahaʻa taimi ʻe uofulu pea ʻe paasi ha taha. Siviʻi ha sīpinga ʻe taha ʻaki ha fakakulupu ʻe 37 ʻo e luomeʻangāueLuoKo e taha ʻo e ngaahi luo ʻe 37 ʻoku fakafika ʻi he konga vilo. ʻOku toe ui: slot, cup.Lau kotoa →, fakakulupu ʻe ono ʻo e kongaveʻetekaKongaKo ha konga fakavilo hokohoko ʻo e ngaahi luo ʻi he veʻeteka, ʻoku kehe ia mei ha kulupu ʻi he palani ʻo e tēpile.Lau kotoa → mo e fakakulupu ʻe tolu ʻo e lanu pea ʻe paasi ha meʻa. Ko hono fakaleleiʻi ko hono fili ʻa e sivi kimuʻa pea sio ki he ngaahi fakamatala, fai ia tuʻo taha, pea fakapapauʻi ʻi ha ngaahi fakamatala foʻou. Ko e vakaiʻi lahi ʻoku ne ʻilo ha veʻeteka “hehema” ko e meʻa ia ʻoku faʻa ʻomi ai ʻa e ola.
Mahuʻinga fakahoa ki he lahi
Ko ha sīpinga lahi ʻaupito ʻe lava ke ne ʻai ha kiʻi hehema siʻisiʻi ke mahuʻinga. Ko ha luo ʻoku tō ki ai ʻi he 1/36.5 ʻi he ʻikai ko e 1/37 ko ha palopalema moʻoni ia ʻe aʻu ki he mahuʻinga ʻi ha vilo ʻe miliona siʻi pea ʻe kei mole ai pē ʻa e paʻanga ʻi ha totongipaʻangaTotongiKo e meʻa ʻoku fakafoki ʻe ha peti ikuna, ʻoku fakahā ko e “X ki he 1” ʻi ʻolunga ʻi he peti ʻoku fakafoki.Lau kotoa → ʻo e 35 ki he 1. Ko e meʻa ʻoku mahuʻinga ki ha tokotaha vaʻinga ko e lahi ʻo e ola: ʻoku tō ki ha luo ʻi he 1/36 pe lelei ange, pea ʻaki ha lahi fēfē? ʻOku tala atu ʻe he chi-square ʻa e meʻa ki he veʻeteka; ko e tuʻo lahi ʻo e tō pē ʻoku ne tala atu ʻa e meʻa ki he peti.
Mālohi
Ko e fehalaaki ʻe taha ko hono taʻe ʻiloʻi ha hehema ʻoku ʻi ai. ʻI ha vilo ʻe 1,000, ko ha luo ʻi he 1/30 (ko ha hehema lahi ʻaupito) ʻoku ʻiloʻi pē ia ʻi he meimei vaeua ʻo e taimi ʻi he tuʻunga ʻo e 5%. Ko e lahi ʻo e sīpinga, ʻo ʻikai ko e poto, ʻoku ne fakaleleiʻi eni. ʻOku ʻomi ʻe he peesi ʻo e lahi ʻo e sīpinga ʻa e ngaahi fika.
Ko ha tuʻunga ngāueʻaki
Ke mahuʻinga ha taukave ʻo ha hehema: ko ha sivi naʻe fili kimuʻa, p < 0.01 ʻi he ʻikai ko e 0.05, toe fai ʻi ha sīpinga tauʻatāina ʻo ha lahi meimei tatau, mo ha fakafuofua ʻo e tuʻo lahi ʻo e tō ki he ngaahi luo ʻoku tō lahi ki ai ʻo e 1/34 pe lelei ange hili hono toe fai. Kuo aʻu ki he tuʻunga ko ia ʻo tuʻo siʻi pē ʻi he hisitōlia ʻo e vaʻinga pea ʻikai ha taimi, ʻo fakatatau ki he ngaahi lēkooti ʻoku ʻatā ki he kakai, ʻi ha veʻeteka ʻo onopooni ʻoku tauhi lelei.
Ngaahi fehuʻi
Ko ha angamaheni mei he ngaahi taʻu 1920. ʻOku ʻikai ha meʻa makehe ai; ko e 0.01 ko ha tuʻunga ʻoku fakapotopoto ange ʻi he taimi ʻoku ke vakaiʻi ai ha ngaahi veʻeteka lahi.
ʻOku ngalingali ʻoku ʻikai ʻomi ʻe ia ha ngaahi ola tatau. ʻE lava ko ha ola ʻo e tīla, ha fehalaaki ʻi hono tohi, pe ha palopalema ʻi hono hū ʻo e ngaahi fakamatala. Toe fai.
ʻIkai. ʻOku ne tala atu ʻoku ʻikai tonu ʻa e tufaki. Ko e vakaiʻi ʻo e ngaahi konga mo e lahi ʻo e ola ʻoku na tala atu ʻa e feituʻu.
Vaʻinga mo e Matematika
ʻUluaki feinga ke ke fakaleleiʻi ʻe koe. Kuo pelu ʻa e tali takitaha; fakaava ia ʻi hoʻo mateuteu.
ʻI ha veʻeteka noaveʻetekaNoaKo e luo lanu mata pē ʻe taha ʻoku ʻikai kāpui ʻe ha peti totongi tatau, peti tasini pe peti kōlomu; ko e tupuʻanga ia ʻo e tuʻunga lelei ʻo e kasino. ʻOku toe ui: noa ʻe taha, 0.Lau kotoa → ua naʻe lipooti, naʻe hā ʻa e ʻuluaki tasinipetiTasini1–12, 13–24 pe 25–36, totongi ʻo e 2:1.Lau kotoa → tuʻo 742 ʻi he vilo ʻe 3,000. ʻOku fiha ha mavahe fakasitanatematematikaMavahe fakasitanateAka ua ʻo e vēliani; ko e mamaʻo angamaheni ʻo ha ola mei he mahuʻinga ʻamanekina.Lau kotoa → ʻoku ʻi lalo ai ʻi he ʻavalisi, pea ʻoku fai ia ʻe ha veʻeteka faitotonu tuʻo fiha?
Fakahā ʻa e tali
Tali Ko e mavahe fakasitanate ʻe 8.1 nai ʻi lalo. ʻE fai ia ʻe ha veʻeteka faitotonu tuʻo taha nai ʻi he feinga ʻe 3 × 10¹⁵, ʻa ia ko e ʻikai ʻaupito. ʻOku pehē ʻe he tali naʻe pulusi mo e fehuʻi ko e 11.75; ʻoku mau maʻu ʻa e 8.07.
ʻOku ʻi he ʻuluaki tasini ʻa e 12 ʻi he luomeʻangāueLuoKo e taha ʻo e ngaahi luo ʻe 37 ʻoku fakafika ʻi he konga vilo. ʻOku toe ui: slot, cup.Lau kotoa → ʻe 38. ʻI he vilo ʻe 3,000 ko hono ʻavalisi ko e tonu ʻe 3,000 × 12/38 = 947.4, mo ha mafolalahi ʻo e √(3,000 × 12/38 × 26/38) = 25.5.
Ko e 742 ʻoku 205.4 ʻi lalo ʻi he ʻavalisi: 205.4/25.5 = mafolalahi ʻe 8.07.
ʻOku tō ha veʻeteka faitotonu ʻo siʻi ʻaki ha mafolalahi ʻe tolu tuʻo taha nai ʻi he feinga ʻe 740; siʻi ʻaki ha mafolalahi ʻe valu, tuʻo taha nai ʻi he 3 × 10¹⁵ (kalava fakafaʻafaʻa, tafaʻaki ʻe taha). Ko hono lau ʻo e meʻa naʻe fakatokangaʻi ʻe he tokotaha lau ko e kovi taha ʻo e tasini ʻe tolu ʻoku ʻikai ke ne liliu ha meʻa mahuʻinga. Ko ha ola pehē ʻoku ne pehē ʻoku hala ʻa e veʻeteka, pe ko e lau. ʻI ha veʻeteka noa ʻe taha ko e lau tatau ʻe mafolalahi ʻe 9.0 ia ʻi lalo (ʻavalisi 973.0, mafolalahi 25.6).
Meʻa fakaoli
Ko e taha ʻi he veʻeteka faitotonu ʻe uofulu ʻoku “mahuʻinga”. Ko e ʻuhinga ia ʻo e fika ko ia.
Ngaahi Maʻuʻanga
- Pearson, K. “On the criterion that a given system of deviations from the probable…”
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Wizard of Odds. “Ask the Wizard”, ngaahi fehuʻi ki he lulēti.