Question

a researcher measured the shoe size and math ability of a large group of children. he found that having a larger shoe size does not indicate that a child has more or less math ability. what does this analysis show? there is no correlation between shoe size and math ability. there may or may not be causation. further studies would have to be done to determine this. 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 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 may or may not be causation. further studies would have to be done to determine this. juan compared the player statistics from his teams tennis season. he determined that being taller implies that a player has faster serves. what should he say based on his findings? there is no 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) Correlation doesn't imply causation. Just because there's a link between shoe - size and math ability doesn't mean one causes the other.
(b) Similarly, in the grocery data, correlation between rice and bread purchases isn't causation.
(c) Height and serve speed correlation isn't causation either. Further study needed for causation.

Answer:

(a) There is no 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. 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.