Question

this question has two parts. first, answer part a. then, answer part b.
part a
frozen desserts the table shows the number of pounds of frozen yogurt and the number of pounds of sherbet consumed per capita in the united states from 2009 to 2016.

a. graph the ordered pairs (pounds of frozen yogurt, pounds of sherbet) to create a scatter plot on a separate sheet of paper.
b. determine whether there is a correlation between the variables in the data. explain.
the scatter plot shows a positive correlation because as the number of pounds of frozen yogurt consumed increases, the number of pounds of sherbet consumed decreases.
part b
c. if there is a correlation, does this mean that a change in time spent reading causes a change in time spent watching television? explain your reasoning.

Explanation:

• Part A (b): Correlation is a relationship between two variables. A negative correlation means that as one variable increases, the other decreases. Here, as pounds of frozen yogurt (one variable) increases, pounds of sherbet (the other variable) decreases.
• Part B: Correlation does not imply causation. Just because two variables (pounds of frozen yogurt and pounds of sherbet) have a correlation (in this case, negative), it doesn't mean that one variable (e.g., change in frozen - yogurt consumption) causes the change in the other variable (sherbet consumption). There could be other factors (like marketing campaigns for one product, health trends affecting one product more than the other etc.) that influence the consumption of each dessert independently or in a non - causal related way.

Answer:

• Part A (b): The scatter plot shows a negative correlation because as the number of pounds of frozen yogurt consumed increases, the number of pounds of sherbet consumed decreases.
• Part B: No. Correlation does not imply causation. There could be other external factors (such as marketing, health trends specific to each product) that affect the consumption of frozen yogurt and sherbet independently, rather than a direct cause - and - effect relationship between the two consumption amounts.