Beschrijvende en inferentiële statistiek (S_BIS)
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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:
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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