Question 1005956: 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 $50,000 485 385 870
Income below $50,000 65 65 130
Total 550 450 1,000
Based on these data, are "being male" and "earning over $50,000" independent events? (5 points)
Yes, P(being male | the person earns over $50,000) ≠ P(being male)
Yes, P(being male | the person earns over $50,000) = P(being male)
No, P(being male | the person earns over $50,000) ≠ P(being male)
No, P(being male | the person earns over $50,000) = P(being male)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Table of values (given)
| Male | Female | Total |
|---|
| Income over $50,000 | 485 | 385 | 870 |
|---|
| Income below $50,000 | 65 | 65 | 130 |
|---|
| Total | 550 | 450 | 1000 |
|---|
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Let's calculate P(being male | the person earns over $50,000)
P(being male | the person earns over $50,000) = (# of males who earn over $50,000)/(# of people who earn over $50,000)
P(being male | the person earns over $50,000) = (485)/(870)
P(being male | the person earns over $50,000) = 0.55747126436781
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Let's calculate P(being male)
P(being male) = (# of males)/(# of people)
P(being male) = (550)/(1000)
P(being male) = 0.55
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Summary so far:
P(being male | the person earns over $50,000) = 0.55747126436781
P(being male) = 0.55
We see that P(being male | the person earns over $50,000) ≠ P(being male)
So the two events are NOT independent. If they were independent, then the probabilities above would be equal.
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Final Answer: Choice C) No, P(being male | the person earns over $50,000) ≠ P(being male)
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