Free Essay

Information

In: Other Topics

Submitted By jfm09
Words 510
Pages 3
Case:
Nedstående tabel viser en fordeling af favorit pizzeriaer, for 165 tilfældigt udvalgte Just Eat brugere. Just Eat informerer at fordelingen er lige stor. Pizzeria | Pizza kebabhuset | Stjernegrillen | Hassans pizza | Mama rosa | Hollywood | Antal | 23 | 30 | 52 | 29 | 31 |
(disse er fiktive informationer).

Goodness of fit:
Goodness-of-fit er en x2-test. Vi benytter Goodness-of-fit, hvis vi ønsker at undersøge om et sæt data passer med en given fordeling. Det udregnes således.
Vi opskriver tabellen med de observerede værdier fra stikprøven. De beregnes vha. nedstående formel: forventet værdi=samlet antal·forventet antal
Altså har vi fx en samlet stikprøve på 433 børn, og det forventede antal overvægtige børn er på 26%. Vil den forventede antal overvægtige børn være 0,26·433=112,58
Derefter beregner man de relative kvadratafvigelser RKA for hver tabelindgang. Dette udregnes via. Nedstående formel:
RKA=forventet værdi-obseveret værdi2forventet værdi
Derefter lægges alle de relative kvadratafvigelser sammen, for at få χ2-teststørrelsen.
Antal frihedsgrader beregnes vha. formlen, n=antal frihedsgrader=antal kategorier-1

Vi finder nu testsandsynligheden, vha. GeoGebra.

Vi vælger funktionen ”sandsynlighedslommeregner”, hvorefter vi vælger ”Chi i anden”. Vi indsætter vores antal frihedsgrader, som i dette tilfælde er 6. Vi indtastede derefter vores χ2-teststørrelse, og fik i dette tilfælde en testsandsynligheden på p=0,043.

Udregning af case:
Til udregning af vores case, er en nulhypotese påkrævet. Vores nulhypotese lyder såldeses:
H0= der er ingen forskel mellem fordeling, af favorit pizzeriaer, i Ikast.
Til udregning af vores case benytter vi x2-regnemetoden, goodness-of-fit, fordi vi kun har et parameter fra én stikprøve. Pizzeria | Pizza kebabhuset | Stjernegrillen | Hassans pizza | Mamma rosa | Hollywood | Antal | 23 | 30 | 52 | 29 | 31 |
Overover ses de observerede værdier.
Vi anvender nedstående formel, til udregning af de forventede værdier: forventet værdi=samlet antal·forventet antal
Det forventede antal er herunder 20% / 15, da vi har 5 forskellige pizzeriaer. Pizzeria | Pizza kebabhuset | stjernegrillen | Hassans Pizza | Mamma rosa | Hollywood | Forventede værdier: | 165·20%=33 | 165·20%=33 | 165·20%=33 | 165·20%=33 | 165·20%=33 |

Nu beregner vi de relative kvadratafvigelser (RKA), for hvert pizzeria vha. nedstående formel:
RKA=forventet værdi-obseveret værdi2forventet værdi
Pizza kebabhuset:
RKA=33-23233=3,030303
Stjernegrillen:
RKA=33-30233=0,2727273
Hassans Pizza:
RKA=33-52233=10,93939
Mamma rosa:
RKA=33-29233=0,4848485
Hollywood:
RKA=33-31233=0,1212121
Vi lægger nu alle de relative kvadratafvigelser sammen, for at få χ2-teststørrelsen: χ2=3,030303+0,2727273+10,93939+0,4848485+0,1212121=14,84848 Nu finder vi antallet af frihedsgrader, vha. nedstående formel: n=antal pizzeriaer-1
Vi indsætter nu vores værdier: n=5-1=4 Vi finder nu p-værdien

Ovenover ses et screenshot, fra GeoGebra. Vi vælger funktionen ”sandsynlighedslommeregner”, hvorefter vi vælger ”Chi i anden”. Vi indsætter vores antal frihedsgrader, som er 4. Vi indtastede derefter vores χ2-teststørrelse, og fik testsandsynligheden p=0,005.

Da vi har valgt et signifikansniveau på 5%, og vores testsandsynlighed er på 0,5% kan vi ikke godkende nulhypotesen. Altså er der ikke en lige fordeling af favorit pizzeriaer, i Ikast.

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