Q.72 - The Practice of Statistics for AP

Question

Are the events “in the labor force” and “college graduate” independent? Justify your answer .

Step-by-Step Solution

Answer

Two events are not independent events.

Step 1: Given information

In the language of government statistics, you are “in the labor force” if you are available for work and either working or actively seeking work. The unemployment rate is the proportion of the labor force (not of the entire population) who are unemployed. Here are data from the Current Population Survey for the civilian population aged $25$years and over in a recent year. The table entries are counts in thousands of people.

We need to find that whether the events “in the labor force” and “college graduate” independent

Step 2: Explanation

It is known that; two events $\mathrm{A}$ and $\mathrm{B}$ can be considered as independent if:

$P(A\mid B)=P\left(A\right)$ 

The probabilities could be calculated as:

$$\begin{gathered} P(\text{ Labor force }\mid \text{ College graduate })=\frac{125133}{186667} \\ =0.6704 \end{gathered}$$

$$\begin{gathered} P\left(\text{ Labor foce }\right)=\frac{125133}{186667} \\ =0.6704 \end{gathered}$$

Here

$P\text{ (Labor force| College graduate) }\ne P\text{ (Labor force) }$

$0.7830\ne 0.6704$

Thus, two events are not independent events.