Question

(a) a car dealership conducted a survey. it showed that a younger customer tended to purchase a lower priced car. what is likely true?
○ there is no correlation between age and purchase price.
○ there is a correlation between age and purchase price. there may or may not be causation. further studies would have to be done to determine this.
○ there is a correlation between age and purchase price. there is probably also causation. this is because there is a decrease in the purchase price with a decrease in age.

(b) a doctor’s office found that a lower outside temperature did not indicate a change in the number of appointments made. what can we determine from this information?
○ there is no correlation between outside temperature and number of appointments made.
○ there is a correlation between outside temperature and number of appointments made. however, there is no causation. this is because there is likely an increase in the number of appointments made with a decrease in the temperature outside.
○ there is a correlation between outside temperature and number of appointments made. there may or may not be causation. further studies would have to be done to determine this.

(c) a piano instructor examined student progress. she noticed that when students spend less time playing video games, their memorization ability does not tend to change. what can she conclude?
○ there is no correlation between amount of time spent playing video games and memorization ability.
○ there is a correlation between amount of time spent playing video games and memorization ability. there is probably also causation. this is because there is an increase in memorization ability with a decrease in the amount of time spent playing video games.
○ there is a correlation between amount of time spent playing video games and memorization ability. there may or may not be causation. further studies would have to be done to determine this.

Explanation:

Part (a)

The survey shows a trend (younger → lower - priced car), so there's a correlation. Causation isn't proven yet (other factors like income, preference could be involved), so further study is needed to determine causation. The first option is wrong (there is a correlation), the third assumes causation too quickly.

The doctor’s office found no indication of a change in appointments with temperature change, meaning there's no correlation between outside temperature and number of appointments. The other options assume a correlation exists, which is incorrect.

When video - game time decreases, memorization ability doesn't tend to change, so there's no correlation between the two. The other options assume a correlation, which is not supported by the observation.

Answer:

There is a correlation between age and purchase price. There may or may not be causation. Further studies would have to be done to determine this.

Part (b)