Question

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1. kiran collects data about the number of trees on property of different schools and the average standardized test scores for those schools. kiran says, “the scatter plot between the number of trees on a school property and student standardized tests scores shows a strong and positive correlation. an increase in the number of trees on school property causes the students to score better on standardized tests.”

a. what does having a strong correlation mean for the relationship between the variables in this situation?
b. what does having a positive correlation mean for the relationship between the variables in this situation?
c. what is wrong with the last sentence of kirans statement? explain your reasoning.

Explanation:

a. A strong correlation means that the number of trees on school property and average standardized test scores have a very close, consistent linear relationship; the data points on the scatter plot cluster tightly along a trend line.
b. A positive correlation means that as the number of trees on school property increases, the average standardized test scores also tend to increase, and vice versa.
c. Kiran confuses correlation with causation. A strong positive correlation only shows that the two variables tend to move together, it does not prove that adding trees directly causes students to score better on tests. There could be other confounding variables (like school funding, student demographics) that explain both the higher tree count and better test scores.

Answer:

1. a. The two variables have a very close linear relationship, with data points tightly clustered on a trend line.
2. b. As the number of trees increases, average test scores also tend to increase.
3. c. Kiran incorrectly assumes correlation equals causation; correlation does not prove more trees directly cause better test scores.