The following table shows the number of active military personnel in 2009, by region (including the District of Columbia).

a. Calculate the mean and standard deviation for the population.
b. Now take 10 samples of size 3 from the population. Use either simple random sampling or systematic sampling with the help of the table of random numbers in Appendix A. Calculate the mean for each sample.
c. Once you have calculated the mean for each sample, calculate the mean of means (i.e., add up your 10 sample means and divide by 10). How does this mean compare with the mean for all states?
d. How does the value of the standard deviation that you calculated in Exercise 8a compare with the value of the standard error (i.e., the standard deviation of the sampling distribution)?
e. Construct two histograms, one for the distribution of values in the population and the other for the various sample means taken from Exercise 8b. Describe and explain any differences you observe between the two distributions.
f. It is important that you have a clear sense of the population that we are working with in this exercise. What is the population?

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Pacific West North Central South Atlantic 89,816 West South Central 177,336 68,440 8,579 229,634 Mountain 64,564 East North Central 26,384 East South Centra 376,034 Middle Atlantic 41,441 New England