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Given the population 4,5,6,7, and 8. Suppose samples of size 3 are drawn from this population.
a. What is the mean (u) and standard deviation (o) of the population?
b. How many different samples of size n=3 can be drawn from the population? List them with their corresponding means.
c. Construct the sampling distribution of the sample means.
d. What is the mean of the sampling distribution of the sample means?
e. What is the standard deviation of the sampling distribution of the sample means?
Show that E(s2) = σ2 in simple random sampling, where the sample variance s2 is defined with n - 1 in the denominator and the population variance σ2 is defined with N - 1 in the denominator.
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