The U.S. Census Bureau serves as the leading source of quantitative data about the nation’s people and economy. The following crosstabulation shows the number of households (1000s) and the household income by the highest level of education for the head of household (U.S. Census Bureau website, 2013). Only households in which the head has a high school diploma or more are included. Highest level of Education Under$25,000 $25,000 to $49,999 $50,000 to $99,999 $100,000 and over Total High school graduate 9880 9970 9441 3482 32,773 Bachelor's degree 2484 4164 7666 7817 22,131 Master's degree 685 1205 3019 4094 9003 Doctoral degree 79 160 422 1076 1737 Total 13,128 15,499 20,548 16,469 65,644 a. Develop a joint probability table.b. What is the probability of the head of one of these households having a master’s degree or more education?c. What is the probability of a household headed by someone with a high school diploma earning $100,000 or more?d. What is the probability of one of these households having an income below $25,000?e. What is the probability of a household headed by someone with a bachelor’s degree earning less than $25,000?f. Is household income independent of educational level?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The U.S. Census Bureau serves as the leading source of quantitative data about the nation’s people and economy. The following crosstabulation shows the number of households (1000s) and the household income by the highest level of education for the head of household (U.S. Census Bureau website, 2013). Only households in which the head has a high school diploma or more are included.
| Highest level of Education | Under$25,000 | $25,000 to $49,999 | $50,000 to $99,999 | $100,000 and over | Total |
| High school graduate | 9880 | 9970 | 9441 | 3482 | 32,773 |
| Bachelor's degree | 2484 | 4164 | 7666 | 7817 | 22,131 |
| Master's degree | 685 | 1205 | 3019 | 4094 | 9003 |
| Doctoral degree | 79 | 160 | 422 | 1076 | 1737 |
| Total | 13,128 | 15,499 | 20,548 | 16,469 | 65,644 |
a. Develop a joint
b. What is the probability of the head of one of these households having a
master’s degree or more education?
c. What is the probability of a household headed by someone with a high
school diploma earning $100,000 or more?
d. What is the probability of one of these households having an income
below $25,000?
e. What is the probability of a household headed by someone with a
bachelor’s degree earning less than $25,000?
f. Is household income independent of educational level?
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