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 States, 2008). Develop a joint probability table. What is the probability of a head of household not being a high school graduate? What is the probability of a head of household having a bachelor's degree or more education? What is the probability of a household headed by someone with a bachelor's degree earning $100,000 or more? What is the probability of a household having income below $25,000? What is the probability of a household headed by someone with a bachelor's degree earning less than $25,000? Is household income independent of educational level? An MBA new-matriculants survey provided the following data for 2018 students.

Explanation / Answer

(b)

Out of 73736 household heads, 9961 are not H.S graduate so we have

P(not high school garduate) = 9961 / 73736

(c)

Out of 73736 household heads, 13787+7822 = 21609 having a bachelor's degree or more so we have

P(a bachelor's degree or more) = 21609 / 73736

(d)

There are 5379 household head has bachelor's degree and earning $100,000 or more so we have

P(bachelor's degree and earning $100,000 or more) = 5379 / 73736

and

P(bachelor's degree) = 13787 / 73736

So the required probability is

P(earning $100,000 or more | bachelor's degree) =P(bachelor's degree and earning $100,000 or more) / P(bachelor's degree) = 5379 / 13787

(e)

Out of 73736 household heads, 13106 have income below $25,000 so we have

P(below $25,000) = 13106 / 73736

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