A researcher measured the shoe size and math ability of a large group of children.

Question

She found that having a larger shoe size does not indicate that a child has more or less math ability. What does her analysis show?
•There is no correlation between shoe size and math ability.
•There is a correlation between shoe size and math ability. There may or may not be causation. Further studies would have to be done to determine this.
•There is a correlation between shoe size and math ability. There is probably also causation.
This is because there is likely an increase in math ability with an increase in shoe size.
A grocery store collected sales data. It found that when customers buy less bread, they tend to purchase more rice. What can we conclude?
•There is no correlation between amount of bread bought and amount of rice purchased.
•There is a correlation between amount of bread bought and amount of rice purchased.
However, there is no causation. This is because there is an increase in the amount of rice purchased with a decrease in the amount of bread bought.
•There is a correlation between amount of bread bought and amount of rice purchased.
There may or may not be causation. Further studies would have to be done to determine this.
Donna compared the player statistics from her team's tennis season. She determined that being taller implies that a player has faster serves. What should she say based on her findings?
•There is no correlation between height and serve speed.
•There is a correlation between height and serve speed. There may or may not be causation.
Further studies would have to be done to determine this.
OThere is a correlation between height and serve speed. However, there is no

Answer 1

Let's analyze each scenario one by one based on the information provided.

1. Researcher measuring shoe size and math ability:

   • The researcher found that having a larger shoe size does not indicate that a child has more or less math ability. This indicates that:
   • There is no correlation between shoe size and math ability.

2. Grocery store sales data:

   • The store found that when customers buy less bread, they tend to purchase more rice. This suggests that:
   • There is a correlation between the amount of bread bought and the amount of rice purchased. However, there is no causation. This is because there is an increase in the amount of rice purchased with a decrease in the amount of bread bought.

3. Donna comparing player statistics:

   • Donna found that being taller implies that a player has faster serves. This indicates a correlation, but we cannot conclude causation merely from the data she has:
   • There is a correlation between height and serve speed. There may or may not be causation. Further studies would have to be done to determine this.

So in summary:

1. Shoe size and math ability: No correlation.
2. Bread and rice purchases: Correlation without causation.
3. Height and serve speed: Correlation with an unknown causation.