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Chapter 2: Problem 71

Does It Pay to Get a College Degree? In Exercise 2.21 on page \(58,\) we saw that those with a college degree were much more likely to be employed. The same article also gives statistics on earnings in the US in 2009 by education level. The median weekly earnings for high school graduates with no college degree was \(\$ 626,\) while the median weekly earnings for college graduates with a bachelor's degree was \(\$ 1025 .\) Give correct notation for and find the difference in medians, using the notation for a median, subscripts to identify the two groups, and a minus sign.

Short Answer

Expert verified
The difference in medians between the weekly earnings of high school graduates without a college degree and college graduates with a bachelor's degree is \$399.

Step by step solution

01

Define the Medians

Let's denote the median weekly earnings for high school graduates without a college degree as \(M_{HS}\) and the median weekly earnings for college graduates with a bachelor's degree as \(M_{C}\). According to provided information, we have \(M_{HS} = \$626\) and \(M_{C} = \$1025\).
02

Establish the Formula

Finding the difference between the two medians is simply a matter of subtraction. We want to subtract the median earnings of the high school graduates \(M_{HS}\) from the median earnings of the college graduates \(M_{C}\). The formula is, \(Diff = M_{C} - M_{HS}\).
03

Calculate the Difference

Substitute the given values into the formula, thus \(Diff = \$1025 - \$626 = \$399\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Median Earnings
Median earnings refer to the middle value in a list of earnings sorted from lowest to highest when talking about a specific group. In other words, half of the people earn more than the median, while the other half earns less. This statistical measure provides a good indication of the typical income in a particular demographic. It prevents extreme values from skewing the average, giving a clearer picture of what a typical person might earn in that group.
For example:
  • Median earnings help to show real-world differences in salary between groups with different education levels. This makes it easier to see the impact of education on income.
  • By comparing median earnings across groups, one can assess the economic value of educational attainment.
Understanding this concept is crucial to evaluating how education impacts earnings, as demonstrated in the provided data.
Benefits of a College Degree
A college degree often brings numerous benefits, particularly in terms of boosting one's financial potential. Statistical data regularly shows that individuals with a bachelor's degree typically earn more than those without. The numbers in the original exercise demonstrate this well:
  • College graduates with a bachelor's degree reported median weekly earnings of $1025.
  • High school graduates with no college degree, on the other hand, earned a median of $626 per week.
  • The difference in earnings between the two groups is $399 weekly, or about $20,748 annually, highlighting a significant financial advantage.
Beyond earnings, degree holders often have better employment statistics, more career stability, and opportunities for advancement. These benefits emphasize the long-term value of investing in higher education.
Employment Statistics and Educational Attainment
Employment statistics often reveal a strong correlation between educational attainment and the likelihood of being employed. Generally, the higher the education level, the better the employment prospects. Key insights from employment statistics include:
  • College graduates tend to have lower unemployment rates compared to non-degree holders.
  • They are more likely to find positions aligned with their field of study.
  • Higher education often leads to more job satisfaction and career progression opportunities.
These trends emphasize the importance of education in improving job prospects. In periods of economic uncertainty or recession, the value of a college degree in terms of securing employment becomes even more pronounced. Understanding this correlation can be a vital factor in making educational decisions.

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Most popular questions from this chapter

The Honeybee dataset contains data collected from the USDA on the estimated number of honeybee colonies (in thousands) for the years 1995 through 2012.77 We use technology to find that a regression line to predict number of (thousand) colonies from year (in calendar year) is $$\text { Colonies }=19,291,511-8.358(\text { Year })$$ (a) Interpret the slope of the line in context. (b) Often researchers will adjust a year explanatory variable such that it represents years since the first year data were colleected. Why might they do this? (Hint: Consider interpreting the yintercept in this regression line.) (c) Predict the bee population in \(2100 .\) Is this prediction appropriate (why or why not)?

Runs and Wins in Baseball In Exercise 2.150 on page \(104,\) we looked at the relationship between total hits by team in the 2014 season and division (NL or AL) in baseball. Two other variables in the BaseballHits dataset are the number of wins and the number of runs scored during the season. The dataset consists of values for each variable from all 30 MLB teams. From these data we calculate the regression line: \(\widehat{\text { Wins }}=34.85+0.070(\) Runs \()\) (a) Which is the explanatory and which is the response variable in this regression line? (b) Interpret the intercept and slope in context. (c) The San Francisco Giants won 88 games while scoring 665 runs in 2014. Predict the number of games won by San Francisco using the regression line. Calculate the residual. Were the Giants efficient at winning games with 665 runs?

Data from the StudentSurvey dataset are given. Construct a relative frequency table of the data using the categories given. Give the relative frequencies rounded to three decimal places. Of the 361 students who answered the question about the number of piercings they had in their body, 188 had no piercings, 82 had one or two piercings, and the rest had more than two.

Levels of carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) in the atmosphere are rising rapidly, far above any levels ever before recorded. Levels were around 278 parts per million in 1800 , before the Industrial Age, and had never, in the hundreds of thousands of years before that, gone above 300 ppm. Levels are now over 400 ppm. Table 2.31 shows the rapid rise of \(\mathrm{CO}_{2}\) concentrations over the 50 years from \(1960-2010\), also available in CarbonDioxide. \(^{73}\) We can use this information to predict \(\mathrm{CO}_{2}\) levels in different years. (a) What is the explanatory variable? What is the response variable? (b) Draw a scatterplot of the data. Does there appear to be a linear relationship in the data? (c) Use technology to find the correlation between year and \(\mathrm{CO}_{2}\) levels. Does the value of the correlation support your answer to part (b)? (d) Use technology to calculate the regression line to predict \(\mathrm{CO}_{2}\) from year. (e) Interpret the slope of the regression line, in terms of carbon dioxide concentrations. (f) What is the intercept of the line? Does it make sense in context? Why or why not? (g) Use the regression line to predict the \(\mathrm{CO}_{2}\) level in \(2003 .\) In \(2020 .\) (h) Find the residual for 2010 . Table 2.31 Concentration of carbon dioxide in the atmosphere $$\begin{array}{lc}\hline \text { Year } & \mathrm{CO}_{2} \\ \hline 1960 & 316.91 \\ 1965 & 320.04 \\\1970 & 325.68 \\ 1975 & 331.08 \\\1980 & 338.68 \\\1985 & 345.87 \\\1990 & 354.16 \\ 1995 & 360.62 \\\2000 & 369.40 \\ 2005 & 379.76 \\\2010 & 389.78 \\ \hline\end{array}$$

Give the relevant proportion using correct notation. A recent headline states that "45\% Think Children of Illegal Immigrants Should Be Able to Attend Public School." The report gives the results of a survey of 1000 randomly selected likely voters in the US.
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