An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would cause shoppers to spend more on groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shopper's family and their grocery bill for that week. The gender of each shopper was also obtained. The data below are expenditures and income for 10 selected survey participants. The correlation for these data is given by:
A)0.649.
B)-0.649.
C)0.4212.
D)-0.4212.

Question

An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would cause shoppers to spend more on groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shopper's family and their grocery bill for that week. The gender of each shopper was also obtained. The data below are expenditures and income for 10 selected survey participants.  The correlation for these data is given by:
A)0.649. 
B)-0.649. 
C)0.4212. 
D)-0.4212.

Quizplus · Accepted Answer

The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the variables are weekly income and weekly grocery expenditures. A correlation coefficient value of 1 indicates a perfect positive linear relationship, while a value of -1 indicates a perfect negative linear relationship. A value of 0 indicates no linear relationship. The range of possible values for correlation coefficient is between -1 and 1.

Based on the given data set, the correlation coefficient is 0.649. This positive value indicates a moderately strong positive linear relationship between weekly income and weekly grocery expenditures. Therefore, as income increases, so does grocery expenditure. The best choice is A) 0.649.

An Economist Conducted a Study of the Possible Association Between