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:
[tex]Male = 20+15+17[/tex]
[tex]Male = 52[/tex]
[tex]Favor = 20 + 18[/tex]
[tex]Favor = 38[/tex]
[tex]Total = 20+15+17+18+12+7[/tex]
[tex]Total = 89[/tex]
Calculate P(Male)
[tex]P(Male) = \frac{Male}{Total}[/tex]
[tex]P(Male) = \frac{52}{89}[/tex]
Calculate P(Favor)
[tex]P(Favor) = \frac{Favor}{Total}[/tex]
[tex]P(Favor) = \frac{38}{89}[/tex]
Calculate P(Male and Favor)
[tex]P(Male\ and\ Favor) = \frac{Male\ and\ Favor}{Total}[/tex]
[tex]P(Male\ and\ Favor) = \frac{20}{89}[/tex]
[tex]P(Male\ and\ Favor) = 0.2247[/tex]
The events are independent is:
[tex]P(Male\ and\ Favor) =P(Male) * P(Favor)[/tex]
So, we have:
[tex]P(Male\ and\ Favor) =\frac{52}{89} * \frac{38}{89}[/tex]
[tex]P(Male\ and\ Favor) =\frac{52*38}{89*89}[/tex]
[tex]P(Male\ and\ Favor) =\frac{1976}{7921}[/tex]
[tex]P(Male\ and\ Favor) =0.2495[/tex]
By comparison:
[tex]P(Male\ and\ Favor) =0.2495[/tex] and [tex]P(Male\ and\ Favor) = 0.2247[/tex] are not equal
Hence, the events are not independent
