[NW] Television Stations and Life Expectancy Based on data obtained from the CIA World Factbook, the linear correlation coefficient between the number of television stations in a country and the life expectancy of residents of the country is 0.599. What does this correlation imply? Do you believe that the more television stations a country has, the longer its population can expect to live? Why or why not? What is a likely lurking variable between number of televisions and life expectancy?

Verified step by step guidance

1. Understand that the linear correlation coefficient, denoted as \(r\), measures the strength and direction of a linear relationship between two variables. Here, \(r = 0.599\) indicates a moderate positive linear relationship between the number of television stations and life expectancy.
2. Interpret the meaning of this correlation: a positive value means that as the number of television stations increases, life expectancy tends to increase as well. However, correlation does not imply causation, so this does not mean that having more television stations causes people to live longer.
3. Consider why the correlation does not imply a causal relationship. There could be other factors influencing both variables, or the relationship could be coincidental. For example, a country with more resources might have both more television stations and better healthcare, which increases life expectancy.
4. Identify a likely lurking variable, which is an unobserved variable that affects both the number of television stations and life expectancy. A plausible lurking variable here is the country's level of economic development or wealth, as wealthier countries tend to have more television stations and higher life expectancy due to better healthcare and living conditions.
5. Summarize that while the correlation shows an association, it is important to investigate underlying factors and not assume a direct cause-and-effect relationship between the number of television stations and life expectancy.

Key Concepts

Correlation Coefficient

The correlation coefficient measures the strength and direction of a linear relationship between two variables, ranging from -1 to 1. A value of 0.599 indicates a moderate positive correlation, meaning as one variable increases, the other tends to increase as well. However, correlation does not imply causation.

Causation vs. Correlation

Causation means one variable directly affects another, while correlation only shows a relationship without proving cause. Just because two variables are correlated does not mean one causes the other; other factors or coincidences may explain the association.

Lurking Variable

A lurking variable is an unobserved factor that influences both variables in a study, potentially explaining their correlation. In this case, factors like a country's economic development or healthcare quality could affect both the number of television stations and life expectancy.