Question

(a) a phone company determined that a higher income indicates that a customer has a more expensive calling plan. what does the analysis show?
there is no correlation between income and calling plan price.
there is a correlation between income and calling plan price. there may or may not be causation. further studies would have to be done to determine this.
there is a correlation between income and calling plan price. there is probably also causation. this is because there is an increase in the calling plan price with an increase in income.

(b) a produce stand conducted a study. it showed that a customer does not tend to buy more or less fruit when more samples are offered. what can we conclude?
there is no correlation between amount of fruit bought and number of samples offered.
there is a correlation between amount of fruit bought and number of samples offered. however, there is no causation. this is because there is probably an increase in the amount of fruit bought with an increase in the number of samples offered.
there is a correlation between amount of fruit bought and number of samples offered. there may or may not be causation. further studies would have to be done to determine this.

(c) joe compared the player statistics from his team’s soccer season. he determined that having less playing time implies that a player scores fewer goals. what should he say based on his findings?
there is no correlation between playing time and number of goals.
there is a correlation between playing time and number of goals. there may or may not be causation. further studies would have to be done to determine this.
there is a correlation between playing time and number of goals. however, there is no causation. this is because there is a decrease in the number of goals with a decrease in playing time.

Explanation:

Part (a)

The phone company found a relationship (higher income → more expensive calling plan). Correlation means a relationship, but causation (one causes the other) isn't proven just by correlation. However, since income and calling plan price have a logical link (people with higher income can afford more expensive plans), there's probably causation too. The first option is wrong (there is a correlation), the second is too cautious as the link is logical, so the third option fits.

The study shows customers don't buy more/less fruit with more samples. So there's no relationship (correlation) between the number of samples and fruit bought. The other options suggest a correlation, which is wrong.

Joe found less playing time → fewer goals, so there's a relationship (correlation) between playing time and goals. Causation (playing time causes goal count) isn't proven just by correlation, so we say there may or may not be causation and further studies are needed. The first option is wrong (there is a correlation), the third is wrong as it claims no causation without proof.

Answer:

There is a correlation between income and calling plan price. There is probably also causation. This is because there is an increase in the calling plan price with an increase in income.

Part (b)