# STATISTICS

The ages of the four presidents who were assassinated in office are {56, 49, 58, 46} for Lincoln, Garfield, McKinley, and Kennedy (respectively). Use these ages as the “population for assassinated presidents” and select a random sample (with replacement) of size 2.a. List the 16 possible samples.b. Find the mean of each sample, then construct a table representing the sampling distribution of the sample mean. In the table, combine values of the sample mean that are the same.c. Compare the mean of the population {56, 49, 58, 46} to the mean of the sampling distribution of the mean.d. Do the sample means target the value of the population mean? In general, do sample means make good estimators of population means? Why or why not?e. Find the variance of each sample, then construct a table representing the sampling distribution of the sample variance. In the table, combine values of the sample variances that are the same.f. Compare the variance of the population {56, 49, 58, 46} to the mean of the sampling distribution of the variance.g. Do the sample variances target the value of the population variance? In general, do sample variances make good estimators of population variances? Why or why not?

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