Texas is home to more than one million undocumented immigrants, and most of them are stuck in low-paying jobs. Meanwhile, the state also suffers from a lack of skilled workers. The Texas Workforce Commission estimates that 133,000 jobs are currently unfilled, many because employers cannot find qualified applicants (The Boston Globe, September 29, 2011). Texas was the first state to pass a law that allows children of undocumented immigrants to pay in-state college tuition rates if they have lived in Texas for three years and plan to become permanent residents. The law passed easily back in 2001 because most legislators believed that producing college graduates and keeping them in Texas benefits the business community. In addition, since college graduates earn more money, they also provide the state with more revenue. Carol Capaldo wishes to estimate the mean hourly wage of workers with various levels of education. She collects a sample of the hourly wages (in $) of 30 workers with a bachelor’s degree or higher, 30 workers with only a high school diploma, and 30 workers who did not finish high school. A portion of the data is shown in the accompanying table.
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
Texas is home to more than one million undocumented immigrants, and most of them are stuck in low-paying jobs. Meanwhile, the state also suffers from a lack of skilled workers. The Texas Workforce Commission estimates that 133,000 jobs are currently unfilled, many because employers cannot find qualified applicants (The Boston Globe, September 29, 2011). Texas was the first state to pass a law that allows children of undocumented immigrants to pay in-state college tuition rates if they have lived in Texas for three years and plan to become permanent residents. The law passed easily back in 2001 because most legislators believed that producing college graduates and keeping them in Texas benefits the business community. In addition, since college graduates earn more money, they also provide the state with more revenue. Carol Capaldo wishes to estimate the
| Bachelor's Degree | High School Diploma | No High School Diploma |
| 22.50 | 12.68 | 11.21 |
| 19.57 | 11.23 | 8.54 |
| 24.13 | 19.53 | 12.52 |
| 27.23 | 9.85 | 9.06 |
| 27.00 | 15.76 | 14.21 |
| 28.60 | 12.31 | 13.40 |
| 16.85 | 12.27 | 11.46 |
| 22.70 | 8.57 | 11.22 |
| 26.69 | 11.06 | 9.56 |
| 20.14 | 11.47 | 9.43 |
| 21.33 | 13.38 | 10.98 |
| 18.33 | 9.85 | 10.41 |
| 17.86 | 12.35 | 11.73 |
| 20.47 | 10.68 | 8.28 |
| 21.08 | 10.70 | 8.59 |
| 17.05 | 11.54 | 13.30 |
| 21.70 | 13.55 | 7.91 |
| 22.19 | 17.80 | 12.28 |
| 23.80 | 15.70 | 10.72 |
| 22.30 | 17.50 | 15.97 |
| 22.42 | 6.50 | 10.58 |
| 22.29 | 8.98 | 9.59 |
| 27.43 | 12.14 | 10.92 |
| 23.14 | 8.83 | 9.70 |
| 22.84 | 13.02 | 7.64 |
| 21.86 | 8.90 | 10.39 |
| 29.32 | 13.80 | 4.62 |
| 26.00 | 21.67 | 13.04 |
| 30.53 | 8.74 | 6.29 |
| 21.44 | 7.47 | 10.27 |
In a report, use the information to
-
Calculate
descriptive statistics to compare the hourly wages for the three education levels. -
Construct and interpret 95% confidence intervals for the mean hourly wage at each education level.
- Include mean and standard deviation results when discussing descriptive statistics.
- Discuss the three wage/education levels as if you are reporting findings to a student contemplating college.
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