Question

(a) a computer manufacturer conducted a survey. it showed that a younger customer will not necessarily purchase a lower or higher priced computer. 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 likely a decrease in the purchase price with a decrease in age.
(b) a hospital found that a lower outside temperature indicates a higher number of patient visits. what can we determine from this information?
there is no correlation between outside temperature and number of patient visits.
there is a correlation between outside temperature and number of patient visits. however, there is no causation. this is because there is an increase in the number of patient visits with a decrease in the temperature outside.
there is a correlation between outside temperature and number of patient visits. there may or may not be causation. further studies would have to be done to determine this.
(c) mr. jackson studied his students biology test scores and sleeping habits. he found that students who slept less tended to earn lower scores on the test. what conclusion should he make?
there is no correlation between test score and amount of sleep.
there is a correlation between test score and amount of sleep. there is probably also causation. this is because there is a decrease in a students test score with a decrease in the amount of sleep.
there is a correlation between test score and amount of sleep. there may or may not be causation. further studies would have to be done to determine this.

Explanation:

Part (a)

• Understanding Correlation and Causation:
• Correlation means there is a relationship (either positive or negative) between two variables. Causation means one variable causes the change in the other variable.
• Just because a younger customer does not necessarily buy a lower - priced or higher - priced computer, it means that we cannot say there is a clear relationship (correlation) between age and purchase price. If there was a correlation (either positive or negative), we could say that as age changes, purchase price changes in a predictable way.

Part (b)

• Analyzing the Hospital Data:
• We know that there is a relationship (correlation) since a lower outside temperature is associated with a higher number of patient visits. But we cannot immediately say that the temperature is the cause of the change in the number of patient visits. There could be other factors (e.g., people are more likely to get sick in cold weather, but there could be other confounders like flu seasons etc.). So, we can only say there is a correlation and further studies are needed to check causation.

Part (c)

• Looking at the Student Data:
• Since students who slept less tended to earn lower scores, there is a relationship (correlation) between the amount of sleep and test scores. But we cannot be sure that less sleep is the cause of lower scores. There could be other factors (e.g., students who are less motivated may sleep less and also study less, leading to lower scores). So, we can say there is a correlation and further studies are needed to check causation.

Answer:

a. There is no correlation between age and purchase price.
b. There is a correlation between outside temperature and number of patient visits. There may or may not be causation. Further studies would have to be done to determine this.
c. There is a correlation between test score and amount of sleep. There may or may not be causation. Further studies would have to be done to determine this.