Question

annabelle works in a deli and has been tracking the daily sales of different items over several months. annabelle found that when there was an increase in the number of cups of hot chocolate sold, the number of cups of coffee sold also increased. similarly, when there was a decrease in the number of cups of hot chocolate sold, the number of cups of coffee also decreased.

which of the following is a valid conclusion?

there is no correlation between the sale of hot chocolate and the sale of coffee.
the increase in the sale of hot chocolate caused an increase in the sale of coffee.
the increase in the sale of hot chocolate is correlated to, but not caused by, the sale of coffee.
no conclusion can be drawn about the correlation or causation of the sale of hot chocolate and the sale of coffee.

Explanation:

Analyze the observed relationship

The problem states that when hot chocolate sales increase, coffee sales also increase. Conversely, when hot chocolate sales decrease, coffee sales also decrease. This shows that the two variables move in the same direction.

Determine the type of correlation

Using the Types of Correlation knowledge point, we can identify that because both variables increase and decrease together, there is a positive correlation between the sale of hot chocolate and the sale of coffee.

Evaluate correlation versus causation

An observational study showing that two variables move together establishes correlation, but it does not prove causation. An increase in hot chocolate sales does not directly cause coffee sales to rise; instead, both are likely influenced by an underlying third variable, such as cold weather or seasonal changes.

Select the valid conclusion

We must choose the option that correctly identifies that a correlation exists, but carefully distinguishes it from direct causation.

• Option 1 is incorrect because there is a clear correlation.
• Option 2 is incorrect because it claims direct causation.
• Option 3 is correct because it states they are correlated but not caused by one another.
• Option 4 is incorrect because a clear conclusion about correlation can indeed be drawn.

Answer:

• (A) There is no correlation between the sale of hot chocolate and the sale of coffee.
• (B) The increase in the sale of hot chocolate caused an increase in the sale of coffee.
• (C) The increase in the sale of hot chocolate is correlated to, but not caused by, the sale of coffee. (Correct answer)
• (D) No conclusion can be drawn about the correlation or causation of the sale of hot chocolate and the sale of coffee.