We have population values 26, 32, 41, 50, 58, and 63 population size N=6 and sample size n=5.
Mean of population (μ) =
626+32+41+50+58+63=45
Variance of population
σ2=NΣ(xi−xˉ)2=61064
σ=σ2=61064 The number of possible samples which can be drawn without replacement is NCn=6C5=6.
no123456Sample26,32,41,50,5826,32,41,50,6326,32,41,63,5826,32,63,50,5826,63,41,50,5863,32,41,50,58Samplemean (xˉ)207/5212/5220/5229/5238/5244/5
Xˉ207/5212/5220/5229/5238/5244/5f(Xˉ)1/61/61/61/61/61/6Xˉf(Xˉ)207/30212/30220/30229/30238/30244/30Xˉ2f(Xˉ)42849/15044944/15048400/15052441/15056644/15059536/150
Mean of sampling distribution
μXˉ=E(Xˉ)=∑Xˉif(Xˉi)=45=μ
The variance of sampling distribution
Var(Xˉ)=σXˉ2=∑Xˉi2f(Xˉi)−[∑Xˉif(Xˉi)]2=150304814−(45)2=1501064=nσ2(N−1N−n)The standard error of the sample means is
σXˉ=1501064≈2.6633
Comments
Leave a comment