Question

question 10 of 25

suppose the correlation coefficient between average daily temperature and the amount of sunscreen purchased is 0.94. which statement must be true?

a. as the temperature increases, the amount of sunscreen purchased tends to increase.
b. putting on sunscreen causes temperatures to increase.
c. hotter temperatures cause people to buy more sunscreen.
d. as the temperature increases, the amount of sunscreen purchased tends to decrease.

Explanation:

Analyze the correlation coefficient

The correlation coefficient \(r = 0.94\) is positive and close to \(1\). This indicates a strong positive linear relationship between average daily temperature and the amount of sunscreen purchased.

Evaluate correlation vs. causation

Correlation does not imply causation. Statements B and C claim causal relationships ("causes"), which cannot be definitively concluded from a correlation coefficient alone.

Determine the correct trend

A positive correlation means that as one variable increases, the other variable tends to increase. Therefore, as temperature increases, the amount of sunscreen purchased tends to increase.

Answer:

• (A) As the temperature increases, the amount of sunscreen purchased tends to increase. (Correct answer)
• (B) Putting on sunscreen causes temperatures to increase.
• (C) Hotter temperatures cause people to buy more sunscreen.
• (D) As the temperature increases, the amount of sunscreen purchased tends to decrease.