Question

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

Favor Do not favor
No opinion
Male
20
15
17
Female
18
12
Are the events 'male' and 'favor independent?

Answer 1

Not independent

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) = (Male)/(Total)`

`P(Male) = (52)/(89)`

Calculate P(Favor)

`P(Favor) = (Favor)/(Total)`

`P(Favor) = (38)/(89)`

Calculate P(Male and Favor)

`P(Male\ and\ Favor) = (Male\ and\ Favor)/(Total)`

`P(Male\ and\ Favor) = (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) =(52)/(89) * (38)/(89)`

`P(Male\ and\ Favor) =(52*38)/(89*89)`

`P(Male\ and\ Favor) =(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