Stats Solutions

(Step-by-Step) The table here expands on the one in Exercise 3.18 by providing data on K-12 education variables and populations for all 50 states. Using

Question: The table here expands on the one in Exercise 3.18 by providing data on \(\mathrm{K}-12\) education variables and populations for all 50 states. Using a sample size of \(n=5\), select repeated random samples without replacement from this population of states and calculate the mean number of students per state for each sample. Plot the sample means, thereby generating a simulated sampling distribution for the sample mean for samples of size 5 .

  1. Describe the shape of the simulated sampling distribution. Does it look normal? Why or why not?
  2. Calculate the standard deviation for the set of generated sample means. Is it close to the theoretical value of
\[\frac{\sigma}{\sqrt{n}}=\frac{1,092,340}{\sqrt{5}}=488,509\]

If not, why not?

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