Mean and Variance of Sample Means | S R S W R | S R S W O R.

Описание: The mean and variance of the sampling distribution of the sample mean depend on whether sampling is done with replacement (WR) or without replacement (WOR).

#meanofsamplingdistributionofmeans
#varianceofsamplingdistributionofmeans

1. Sampling with Replacement (wR)

✓ Each selection is independent.
✓ The population size is not considered because samples are drawn with replacement.

2. Sampling without Replacement (woR)

✓ Each selection affects the next (dependent selections).
✓ A finite population correction (FPC) factor is needed.

Major Points

1. Mean is the same for both cases ().
2. Variance is smaller when sampling without replacement due to the FPC factor.
3. If is large, the FPC factor approaches 1, making the difference 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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