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Problem 51 Hard Difficulty

The following crosstabulation shows household income by educational level of the head
of household (Statistical Abstract of the United States, $2008 ) .$
$\begin{array}{l}{\text { a. Develop a joint probability table. }} \\ {\text { b. What is the probability of a head of household not being a high school graduate? }} \\ {\text { c. What is the probability of a head of household having a bachelor's degree or more }} \\ {\text { education? }}\end{array}$
$\begin{array}{l}{\text { d. What is the probability of a household headed by someone with a bachelor's degree }} \\ {\text { earning } \$ 100,000 \text { or more? }} \\ {\text { e. What is the probability of a household having income below } \$ 25,000 ?}\end{array}$
$\begin{array}{l}{\text { f. What is the probability of a household headed by someone with a bachelor's degree }} \\ {\text { earning less than } \$ 25,000 ?} \\ {\text { g. Is household income independent of educational level? }}\end{array}$

Answer

a. See table
b. 0.1351
c. 0.2931
d. 0.3898
e. 0.1777
f. 0.0642
g. $N_{0}$

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Video Transcript

for the following problem. We're given the table to the right picture in blue and I'm told to create a joint probability table using those values. To do this, we take the numbers from the table. So the joint probability of under 25 not a high school graduate. We 4207 divided by the total number of people Simple, which is 73,736 to give a joint probability of 0.571 We do this for each slot in the table to get all of the joint probabilities. We then add all of the values in each row to get the marginal probabilities. So for not a high school graduate for education level, a marginal probability will be 0.571 was 0.0 for 69 plus 0.188 plus 0.73 last 0.5 to give a marginal probability of 0.1351 We repeat that process for each education level, as well as repeating that process for each column, a k a household income. Part B asks what is the probability of a head of household not being a high school graduate. The probability of not being high school graduate is the marginal probability of not being a high school graduate. So looking at our table, that's 0.1351 hurt, See asks, What is the probability of a head of household having a bachelors degree or more? Education is the probability of a bachelor's degree, plus the probability of Beyonce. So this would be the two marginal probabilities added together, looking at the table, that would be 0.187 plus 0.1061 to give a probability of 0.2931 parte de asks, What is the probability of a household headed by someone with a bachelor's degree earning $1000 or more? This is the probability of earning $1000 or more. Given that you have a bachelor's degree, this is equal to the joint probability, the probability of $1000 war and about Cher's degree divided by the marginal probability of having a bachelors degree looking at the table that gives us joint probability of 0.7 to 9, divided by the marginal probability of 0.187 to give a probability of 0.3898 Hurt E asks. What is the probability of a household having an income below 25? This is the marginal probability of having an income lower than 25. Looking at the table that we went 1777 her F asks. Where is the probability of a household headed by someone with a bachelor's degree earning less than 25? This is the probability of under 25 given a bachelor's degree, which is equal to the joint probability divided by the marginal probability of a bachelor's degree. Looking at this table, the joint probability is 0.12 while the marginal probability is 0.187 To give a total probability of 0.642 Hurt G asks his household income independent of education. Looking at the results from part half receive the probability of being under 25 given about truce degree. His 0.642 while looking at the marginal probability of under 25 is 250.1777 Therefore, having a bachelor's degree decreased the probability of having a household income under 25 therefore household income is not independent of education