An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
A scatter plot is more appropriate for displaying the relationship between the number of items purchased and the amount spent.
The association is positive, indicating that as the number of items increases, the amount spent also tends to increase.
The correlation coefficient is approximately 0.79, suggesting a moderately strong association.
Therefore, the relationship is positive, moderately strong, and approximately linear.
Explanation
Understanding the Problem The problem provides a dataset of customer spending habits during the holiday season, recording the number of items purchased and the total amount spent. We need to determine the best way to display this data (scatter plot or line graph) and describe the relationship between the two variables.
Choosing the Right Graph For Part A, we need to choose between a scatter plot and a line graph. Scatter plots are used to visualize the relationship between two quantitative variables, while line graphs are typically used to show trends over time or connect data points in a sequence. In this case, we want to see how the amount spent changes with the number of items purchased, so a scatter plot is more appropriate.
Describing the Association For Part B, we need to describe the association between the number of items purchased and the amount spent. This involves determining if the association is linear or nonlinear, strong or weak, and positive or negative.
Analyzing the Data Based on the data, we can observe that as the number of items purchased increases, the amount spent also tends to increase. This suggests a positive association. To determine if the association is linear or nonlinear and strong or weak, we can calculate the correlation coefficient.
Calculating the Correlation Coefficient The correlation coefficient, calculated using the data, is approximately 0.79. A correlation coefficient close to 1 indicates a strong positive linear association. Therefore, the association between the number of items purchased and the amount spent is positive and moderately strong.
Final Answer In summary, a scatter plot is the more appropriate graph for displaying this data. The association between the number of items purchased and the total amount of money spent is positive, moderately strong, and approximately linear.
Examples
Understanding the relationship between the number of items purchased and the total amount spent can help retailers optimize their marketing strategies. For example, if a strong positive correlation is observed, the retailer might consider offering discounts on bulk purchases to encourage customers to buy more items, knowing that this will likely lead to a higher total spend. Conversely, if the correlation is weak, other factors might be influencing customer spending, and the retailer would need to investigate those factors further to tailor their strategies effectively. This type of analysis can also help in forecasting sales and managing inventory during peak seasons.
