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) Household Income Educational Level Under 25 25.0-49.9 50.0-74.5 75.0-99.9 100 or more Total Not H.S. Graduate 4207 3459 1389 539 367 9961 H.S. Graduate 4917 6850 5027 2637 2668 22099 Some College 2807 5258 4678 3250 4074 20067 Bachelor’s Degree 885 2094 2848 2581 5379 13787 Beyond Bach. Deg. 290 829 1274 1241 4188 7822 Total 13106 18490 15216 10248 16676 73736 1.     Develop a joint probability table. 2.     What is the probability of a head of household not being a high school graduate? 3.     What is the probability of a head household having a bachelor’s degree or more education? 4.     What is the probability of a household headed by someone having bachelors degree earnings $100,000 or more? 5.     What is the probability of a household having income below $25,000 6.     What is the probability of a household headed by someone with bachelor’s degree earnings less than $25,000? 7.     Is household income independent of educational level? The Following crosstabulation shows household income by educational level of the head of household (Statistical Abstract of the United States, 2008) Household Income Educational Level Under 25 25.0-49.9 50.0-74.5 75.0-99.9 100 or more Total Not H.S. Graduate 4207 3459 1389 539 367 9961 H.S. Graduate 4917 6850 5027 2637 2668 22099 Some College 2807 5258 4678 3250 4074 20067 Bachelor’s Degree 885 2094 2848 2581 5379 13787 Beyond Bach. Deg. 290 829 1274 1241 4188 7822 Total 13106 18490 15216 10248 16676 73736 1.     Develop a joint probability table. 2.     What is the probability of a head of household not being a high school graduate? 3.     What is the probability of a head household having a bachelor’s degree or more education? 4.     What is the probability of a household headed by someone having bachelors degree earnings $100,000 or more? 5.     What is the probability of a household having income below $25,000 6.     What is the probability of a household headed by someone with bachelor’s degree earnings less than $25,000? 7.     Is household income independent of educational level?

Explanation / Answer

dividing each cell by 73736 ; below is  joint probability table.

2)

probability of a head of household not being a high school graduate =1-P(high school graduate) =1-0.2997 =0.7003

3)

probability of a head household having a bachelor’s degree or more education =0.0120+0.0039 =0.0159

4)

probability of a household headed by someone having bachelors degree earnings $100,000 or more

=0.0729

5)

probability of a household having income below $25,000 =0.1777

6)

probability of a household headed by someone with bachelor’s degree earnings less than $25,000

=0.0120

7)

No as probability of a household headed by someone with bachelor’s degree earnings less than $25,000 is not equal to multiplication of probability of bachelor degree and probability of earning less than 25000

Educational Level Under 25 25.0-49.9 50.0-74.5 75.0-99.9 100 or more Total Not H.S. Graduate 0.0571 0.0469 0.0188 0.0073 0.0050 0.1351 H.S. Graduate 0.0667 0.0929 0.0682 0.0358 0.0362 0.2997 Some College 0.0381 0.0713 0.0634 0.0441 0.0553 0.2721 Bachelor’s Degree 0.0120 0.0284 0.0386 0.0350 0.0729 0.1870 Beyond Bach. Deg. 0.0039 0.0112 0.0173 0.0168 0.0568 0.1061 Total 0.1777 0.2508 0.2064 0.1390 0.2262 1.0000

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