Question

Use the two way table below to answer the question given.

Answer 1

Answer:

Not independent

Step-by-step explanation:

Given

See attachment for two way table

Required

Are male and favor independent?

From the table, we have:

$Male = 20+15+17$

$Male = 52$

$Favor = 20 + 18$

$Favor = 38$

$Total = 20+15+17+18+12+7$

$Total = 89$

Calculate P(Male)

$P(Male) = \frac{Male}{Total}$

$P(Male) = \frac{52}{89}$

Calculate P(Favor)

$P(Favor) = \frac{Favor}{Total}$

$P(Favor) = \frac{38}{89}$

Calculate P(Male and Favor)

$P(Male\ and\ Favor) = \frac{Male\ and\ Favor}{Total}$

$P(Male\ and\ Favor) = \frac{20}{89}$

$P(Male\ and\ Favor) = 0.2247$

The events are independent is:

$P(Male\ and\ Favor) =P(Male) * P(Favor)$

So, we have:

$P(Male\ and\ Favor) =\frac{52}{89} * \frac{38}{89}$

$P(Male\ and\ Favor) =\frac{52*38}{89*89}$

$P(Male\ and\ Favor) =\frac{1976}{7921}$

$P(Male\ and\ Favor) =0.2495$

By comparison:

$P(Male\ and\ Favor) =0.2495$ and $P(Male\ and\ Favor) = 0.2247$ are not equal

Hence, the events are not independent