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The owner of a chain of supermarkets notices that there is a positive correlation between the sales of beer and the sales of ice cream over the course of the previous year. During seasons when sales of beer were above average, sales of ice cream also tended to be above average. Likewise, during seasons when sales of beer were below average, sales of ice cream also tended to be below average. Which of the following would be a valid conclusion from these facts?

(a) Sales records must be in error. There should be no association between beer and ice cream sales.

(b) Evidently, for a significant proportion of customers of these supermarkets, drinking beer causes a desire for ice cream, or eating ice cream causes a thirst for beer.

(c) A scatterplot of monthly ice cream sales versus monthly beer sales would show that a straight line describes the pattern in the plot, but it would have to be a horizontal line.

(d) There is a clear negative association between beer sales and ice cream sales.

(e) The positive correlation is most likely a result of the lurking variable temperature; that is, as temperatures increase, so do both beer sales and ice cream sales.

Step by step solution

01

Given information

Type of correlation between the sale of beer and sale of ice-cream is positive.

02

Concept

The correlation coefficient indicates the degree to which the two variables are linearly related.

03

Explanation

The relationship between beer and ice cream sales is good. The linear relationship between the variables is defined by correlation. However, correlation does not imply causation, which means that a change in one variable's sale is not caused by another. However, the change could be due to another factor that causes the sales to behave similarly. In the summer, ice cream is in high demand. Beer is also commonly consumed in the summer. As a result, the most common reason of positive correlation is temperature (which acts as a lurking variable).

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