Solve the Problem Consider These Board Members to Be a Population of Interest

question 16

Essay

Solve the problem.
-The ages of six members of a board of directors of a nonprofit organization are shown below.
$\begin{array}{r|cccccc} \text { Member } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \\ \hline \text { Age } & 32 & 52 & 43 & 64 & 41 & 50 \end{array}$
Consider these board members to be a population of interest. The mean age, $\mu$ , for the population is 47. Construct a table that shows all of the possible samples of size five. For each of the possible samples, list the people in the sample, their ages, and the sample mean. The first line of the table is shown below. $\begin{array}{c|c|c} \text { Sample } & \text { Ages } & \bar{x} \\ \hline \text { A }, B, C, D, E & 32,52,43,64,41 & 46.4 \end{array}$
Use your table to find the probability that, for a random sample of size five, the sample mean will be within 2 years of the population mean.

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Definitions:

Case Study

A detailed examination of a single subject (an individual, group, or event), used as a research method to gain in-depth insights.

Correlation

The extent to which two factors vary together, and thus of how well either factor predicts the other. The correlation coefficient is the mathematical expression of the relationship, ranging from −1 to +1.

Dependent Variables

In an experiment, these are the variables that are tested and measured; they depend on the independent variable.

Random Samples

Random samples are a method of selecting a subset of individuals from a population in which each individual has an equal chance of being chosen, used to ensure generalizability of results.