Construct the sampling distribution of the sample mean for the population that consists of the scores 15, 18, 11, 14, 17, with a sample size of 3. Compute as well the mean of the sampling distribution using the expected value of the distribution and verify the result by computing for the population mean.
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Expert's answer
2022-05-19T09:33:12-0400
We have population values 15, 18, 11, 14, 17, population size N=5 and sample size n=3.
Mean of population (μ) = 515+18+11+14+17=15
Variance of population
σ2=nΣ(xi−xˉ)2=50+9+16+1+4=6
σ=σ2=6≈2.4495
Select a random sample of size 3 without replacement. We have a sample distribution of sample mean.
The number of possible samples which can be drawn without replacement is NCn=5C3=10.
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