The following crosstabulation shows household income by educational level of the

Question

The following crosstabulation shows household income by educational level of the head of household (Statistical Abstract of the United Ststes 2008). Your work has to show the steps that you've taken to answer each question. If, irn order to answer any of the questions below, you need to find other probabilities, please show them as well Household Incomes ($1000s) 50-74.9 1,389 5,027 4,678 2,848 1,274 15,216 75-99.9 539 2,637 3,250 2,581 1,241 10,248 100 plus 367 2,668 4,074 5,379 4,188 16,676 Under 25 25.0-49.9 3,459 6,850 5,258 2,094 829 18,490 1. What is the probability of a household headed by someone with a bachelor's degree earning less than Not HS grad 4,207 HS grad 4,917 Some college2,807 885 290 Total 9,961 22,099 20,067 13,787 7,822 73,736 Bachelor's Beyond Bachelor's Total 13,106 $25,000? 2. Explain what type of probability is represented in the crosstabulation above 3. Is having an income of $100,000 or more independent of having a Bachelor's degree? Explain and give evidence for your answer

Explanation / Answer

Answer to the question is as follows:

1.

P( a hoursehold headed by some with bac' degreee earn less than $25,000) = ?

= (885 / 73736)

=0.012

Answer is 0.012

2. Explanation: Out of total 73736 people, we wanted to know people who earned less than $25000 and had bachelors degree. Look to intersection of the 1st column: "Under 25" and the 4th row ( bachelor's) to know how many how many such people exist. This gives us 885. Thus the probability is 885 out of total 73736 people

3.

Event A - earn $100,000+, P(A) = 16676/73736 = 0.226

Event B - has bachelor' degress = 13787/73736 = 0.187

Lets calculate P(A)*P(B) = .226*.187 = 0.0423

P(A and B) = earn $100,000+ and has bachelor' degree = 5379/73736 = 0.073.

Since P(A)*P(B) != P(A and B), we say that events A and B are not independent.

So, having an income of $100000 or more is independent of having a Bachelor' degree

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