Question

The following cross-tabulation shows household income by the educational level of the head of the household (Statistical Abstract of the United States, 2008).

		Household Income ($1000s)
Education Level	Under 25	25.0 –49.9	50.0 – 74.9	75.0 – 99.9	100 or more	Total
Not H.S. Graduate	4,207	3,459	1,389	539	367	9,961
H.S. Graduate	4,917	6,850	5,027	2,637	2,668	22,099
Some College	2,807	5,258	4,678	3,250	4,074	20,067
Bachelor’s Degree	885	2,094	2,848	2,581	5,379	13,787
Beyond Bach. Deg.	290	829	1,274	1,241	4,188	7,822
Total	13,106	18,490	15,216	10,248	16,676	73,736

a. Develop the joint probability table below.

b. What is the probability of a head of household not being a high school graduate?

c. What is the probability of a head of household having a bachelor’s degree or more education?

d. What is the probability of a household headed by someone with a bachelor’s degree earning $100,000 or more?

e. What is the probability of a household having income below $25,000?

f. What is the probability of a household headed by someone with a bachelor’s degree earning less than $25,000?

g. Is household income independent of educational level? Clearly show your work in the space below.

Answer 1

a) doividing each cell value with total frequency of 73736:

Education Level	Under 25	25.0 –49.9	50.0 – 74.9	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

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

=1-(22099/73736)

=0.7003

c)

probability of a head of household having a bachelor’s degree or more education

=(13787+7822)/73736

=0.2931

d)probability of a household headed by someone with a bachelor’s degree earning $100,000 or more

=(5379/73736)

=0.0729

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

f) probability of a household headed by someone with a bachelor’s degree earning less than $25,000 =

0.0120

g)

No, since P(bachelor degree)*P(earning less than 25000) =0.1870*0.1777

=0.0332 is not equal to bachelor’s degree and earning less than $25,000 of 0.0120

therefore events are not independent