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Samenvatting BIS deeltentamen 2 - alle kennisclips :) $6.61   Add to cart

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Samenvatting BIS deeltentamen 2 - alle kennisclips :)

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Alle kennisclip voor het tweede deeltentamen van BIS (ik verkoop ook voor dt1 en dt3) :) succes

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  • September 18, 2024
  • 8
  • 2024/2025
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M6 Betrouwbaarheidsintervallen

Twee typen statistieke inferenties:

- Estimation

Point estimate: 1 nummer die het beste een gok doet over de populatieparameter
(gemiddelde)

Interval estimate: range of values in which we expect the population value to fall
(confidence level (betrouwbaarheidsinterval) = the probability that the interval contains the
population value → always a number close to 1)

- Hypothesis testing (M7)




A proportion of 0,025 corresponds with a z-score of 1,96, which means that there is 95% chance that
the sample proportion will fall within 1,96 standard deviations of the population proportion = marge
of error → formule waarmee je een 95% betrouwbaarheidsinterval kan berekenen is:




Voorbeeld n = 100, p=0,17

se = √(𝑝(1 − 𝑝): 𝑛 = √(0,17(1 − 0,17): 100 = 0,038

Betrouwbaarheidsinterval = 𝑝 ± 𝑍95% (𝑠𝑒)

= 0,17 + 1,96 . 0,038 = 0,24

= 0,17 + 1,96 . 0,038 = 0,10

Betrouwbaarheidsinterval is > 0,10 en < 0,24



Bovenstaande formule kan je alleen gebruiken bij een standaard normaalverdeling waarbij geldt:




gemiddelde
standaarddeviatie steekproef
standaarddeviatie populatie (meestal niet bekend, maar je kan wel de ‘estimated
standard deviation of the sampling distribution of the sample mean’ berekenen) →

, The margin of error tells us to what extent the sample mean (x-bar) is able to estimate the
population mean µ




The t-distribution

- Let op de extra fouten die gemaakt kunnen worden en heeft daarom dikkere staarten met
een hogere standaarddeviatie
- De exacte grootte van de t-distributie hangt af van de grootte van de steekproef → hoe
groter de n, hoe meer de t-distributie lijkt op de normaalverdeling
- Het verloop van de t-distributie is afhankelijk van de ‘degrees of feedom = df = n-1’
o Bij df=30 is de t-d zo goed als identiek aan de normaalverdeling
o Bij een werkelijk identieke normaalverdeling geldt: df=∞

Proportion → look up the z-score
Mean → look up the t-distribution

For a confidence interval, two assumptions need to be considered:

1. Randomization
2. Approximately normal population distribution Met opmerkingen [TL(1]: Bij leren de 6.EXTRA kijken

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