Sampling Distribution of Sample Proportion | Mean and Variance of Proportion | W R Size 2 & 3 .

Описание: The sampling distribution of the sample proportion can be studied in two cases:

1. Sampling with Replacement (Independent Sampling)
2. Sampling without Replacement (Dependent Sampling)

1. Sampling with Replacement

✓ Each selected individual is returned to the population before selecting the next.

✓ The selections are independent (each selection does not affect the next).

✓ The sample proportion (p^) follows an approximately normal distribution for large , with:


E(p^) = p
V(p^) = pq / n
S.E (p^) = √ ( pq / n )

2. Sampling without Replacement

✓ Once an individual is selected, it is not returned to the population.
✓ The selections are dependent (each selection affects the next).

✓ The standard error needs a finite population correction (FPC):

E(p^) = p
V(p^) = pq / n * ( N - n ) / ( N - 1 )
S.E (p^) = √ { pq / n * ( N - n ) / ( N - 1 ) }

where:

N = population size

n = sample size

p = true population proportion

If n is small relative to (typically ), the difference between sampling with and without replacement is negligible.

In this chapter we discuss in detail...

#populationtypesofpopulation
#sampleandpopulation #censusandsurvey
#parameterandstatistic #dataanddatum
#advantagesofsampling #samplingframe #samplingdesign #CLT #probabilityandnonprobabilitysampling #samplingwithreplacement #samplingwithoutreplacement
#samplingandnonsamplingerror
#randomnumbers #samplingbias
#simplerandomsampling
#stratifiedrandomsampling
#systematicrandomsamplimg
#multistagesampling #multiphasesampling
#clusterrandomsampling
#nonprobabilitysampling #qoutasampling #purposivesampling #judgementsampling #snowballsampling #bubblesampling #sequentialsampling #usesofsampling #standarddeviation #standarderror #allocationofsamplesize #proportionalallocation
#optimumallocation #equalallocation #naymanallocation #centrallimittheorem #chebyshevinequalities #samplongdistributionofmeans #samplingdistributionofproportion #randomnumbers #samplingdistributionofvariances

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