Question

one statistic used to measure a countrys wealth is its gross domestic product (gdp). a higher gdp indicates greater wealth in the country. a researcher compared the gdp per person for 12 countries with the life expectancy of that country. the data for the 12 countries are shown in the scatterplot. the value of r for the scatterplot is 0.608. which of the following statements accurately describes the relationship shown in the scatterplot? there is little relationship between gdp and life expectancy. countries with lower gdps tend to have higher life expectancies. countries with higher gdps tend to have lower life expectancies. countries with higher gdps tend to have higher life expectancies.

Explanation:

Step1: Analyze the scatter - plot trend

In a scatter - plot, if the value of the correlation coefficient \(r\) is positive, it indicates a positive linear relationship. That is, as one variable (in this case, GDP per person) increases, the other variable (life expectancy) also tends to increase.

Step2: Evaluate each option

• Option 1: Since \(r = 0.608\) (a non - zero value), there is a relationship. So, "There is little relationship between GDP and life expectancy" is incorrect.
• Option 2: A positive \(r\) value does not support "Countries with lower GDPs tend to have higher life expectancies".
• Option 3: A positive \(r\) value does not support "Countries with higher GDPs tend to have lower life expectancies".
• Option 4: A positive \(r = 0.608\) implies that as GDP per person (a measure of country wealth) increases, life expectancy (the other variable) also has a tendency to increase. So, "Countries with higher GDPs tend to have higher life expectancies" is correct.

Answer:

Countries with higher GDPs tend to have higher life expectancies.