Question

A survey of 1,000 men and women asked, "Do you earn over $50,000 per year?" The table below shows the responses for males and females:

Male Female Total
Income over $50,000 475 375 850
Income below $50,000 75 75 150
Total 550 450 1,000


Based on these data, are "being female" and "earning over $50,000" independent events?

Answer 1

@IMStuck please help

Answer 2

Let the event 'being female' be A, and let the event 'earning over $50,000' be B.
Then events A and B are independent if, and only if:
\[P(A \cap B)=P(A) \times P(B)\]
P(A) = 450/1000 = 0.45
P(B) = 850/1000 = 0.85
\[P(A) \times P(B)=0.45\times0.85=0.3825\]

Answer 3

ok im not good with this but so far i understand

Answer 4

But from the table the probability of being female and earning over $50,000 is 375/1000 = 0.375
So the criterion for independence of A and B is not met, the reason being that:
P(A intersection B) does not equal P(A) * P(B).

Answer 5

THANK YOU!!!!!!!!!!!

Answer 6

You're welcome :)

Answer 7

so it is No, P(being female | the person earns over $50,000) ≠ P(being female)

Answer 8

?

Answer 9

or is it Yes, P(being female | the person earns over $50,000) ≠ P(being female)

Answer 10

The answer is No, "being female" and "earning over $50,000" are not independent events.

Answer 11

thanks!!!

Answer 12

You're welcome :)
Please note that there is a different test for independence to the test that I used. Only one test is necessary.