Question

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

mai compared the player statistics from her teams 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.
○ there is a correlation between height and serve speed. however, there is no causation. this is because there is an increase in serve speed with an increase in height.

Explanation:

(a) A correlation was found between shoe - size and math ability in children, but correlation does not imply causation.
(b) There is a negative correlation between bread and rice purchases in grocery store data, meaning as one decreases, the other increases, but no causation is established.
(c) There is a positive correlation between height and serve - speed in tennis players, but further studies are needed to determine causation.

Answer:

(a) 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.
(b) There is a correlation between amount of bread bought and amount of rice purchased (an increase in one leads to a decrease in the other). There may or may not be causation. Further studies would have to be done to determine this.
(c) 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.