Question

A survey of 1,200 men and women asked, "Do you earn over $75,000 per year?" The table below shows the responses for males and females:

Based on these data, are "being female" and "earning over $75,000" independent events?

Answer 1

Off the top of my head I would say yes, because 1 person being female and earning over 75,000 doesn't directly affect the next person being female and earning over 75,000

Answer 2

Male Female Total
Income over $75,000 585 485 1,070
Income below $75,000 65 65 130
Total 650 550 1200

Answer 3

There we go.

Answer 4

That's what I thought too, but the answer choices are strange.

Answer 5

A. No, P(being female | the person earns over $75,000) = P(being female)

B. No, P(being female | the person earns over $75,000) ≠ P(being female)

C. Yes, P(being female | the person earns over $75,000) = P(being female)

D. Yes, P(being female | the person earns over $75,000) ≠ P(being female)

Answer 6

My instinct says "B".

Answer 7

The second part of the answer is kinda weird though I agree

Answer 8

But the probability of being female and the person earning over $75,000 does not equal the probability of being female. But I need to double check.

Answer 9

All right.

Answer 10

yeah, so the probability of being female is 45%

Answer 11

The probability of being female and earning over 75,000 is 40%

Answer 12

does that seem logical?

Answer 13

I think I get it. And because those two things aren't equal, the situation is dependent?

Answer 14

That doesn't make sense though.... wouldn't it be independent?

Answer 15

well that's what makes this question weird

Answer 16

Independent means that a result doesn't care about what happens earlier. Like flipping a coin. It doesn't matter if you got heads 20 times in a row. The next flip is still 50/50

Answer 17

Dependent means it does care about what happened earlier. Say you have 5 beads in a bag. Each time you pull one out, you're changing the odds of the next pull.

Answer 18

I see..... then this is definitely independent, because it doesn't matter what the person said before them, they still have their answer....

Answer 19

yes

Answer 20

but, based on the table, more males had an income over 75,000 than females.

Answer 21

Ugh, I hate stats.

Answer 22

that's how i see it anyways. but we could not be understanding the problem fully

Answer 23

or think of it this way.

Answer 24

does being a woman automatically affect whether you make more or less than 75K

Answer 25

I think according to the table, no, but on a "moral" level, then the answer is yes

Answer 26

in a perfect world, no, but the table says otherwise....

Answer 27

Screw it. What's your best guess? I'm going for it.

Answer 28

I think D.

Answer 29

@jbell0385

Answer 30

My best guess is B

Answer 31

All right. Thank you! Do you think that you could maybe help me with a couple more? There seems to be less debate over what the question wants.