Solve the Problem. -The Ages (In Years) of the Four U.S. Vice Presidents

question 153

Essay

Solve the problem.
-The ages (in years) of the four U.S. vice presidents who assumed office after presidential assassinations are
56 (A. Johnson), 51 (C. Arthur), 42 (T. Roosevelt), and 55 (L.B. Johnson). (i) Assuming that 2 of the ages are
randomly selected with replacement, list the 16 different possible samples. (ii) Find the standard deviation of
each of the 16 samples, then summarize the sampling distribution of the standard deviation in the format of a
table representing the probability distribution. (iii) Compare the population standard deviation to the mean of
the sample standard deviations. (iv) Do the sample standard deviations target the value of the population
standard deviation? In general, do sample standard deviations make good estimators of population standard
deviations? Why or why not?

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Definitions:

Classification

The process of grouping things based on shared qualities or characteristics.

Nominal Data

Nominal data is a type of categorical data where values or categories cannot be logically ordered or ranked. The data represent labels or names that identify categories of similar items without implying hierarchy.

Arbitrary

Based on random choice or personal whim, rather than any reason or system.

Continuous Data

Data that can take on any value within a given range, as opposed to discrete data which can only take on specific values.