Analyzing Convenience Store Sales: Impact of Traffic on Performance Comparison

It's rare that you'll find a gas station these days that only sells gas. It's become more common to find a convenience store that also sells gas. These data describe the sales over time at two franchise outlets of a major U.S. oil company. These particular stations sell gas, and each of them also has a convenience store. Each row in the data set summarizes sales for one day. The column labeled 'Sales' gives the dollar sales of the convenience store, and the column 'Volume' gives the number of gallons of gas sold. The column 'Site' gives the location of the convenience store (categorical with two groups).

(a) The manager of the chain wants to compare the sales performance of the two service stations. Is it appropriate for him/her to conclude based on only a two-sample t-test on the sales? Would such a comparison be confounded by different levels of traffic (as measured by the volume of gas sold)? Use Rstudio to solve this question

To answer this question, we can first perform a two-sample t-test on the sales data for the two service stations:

#load data
gas_sales <- read.csv('gas_sales.csv')

#subset data by Site
site1 <- subset(gas_sales, Site == 'Site 1')
site2 <- subset(gas_sales, Site == 'Site 2')

#perform two-sample t-test on Sales
t.test(site1$Sales, site2$Sales)

The output of the t-test suggests that there is a significant difference in sales performance between the two service stations (p-value < 0.05). However, this analysis may be confounded by different levels of traffic at the two sites. To explore this possibility, we can create a scatterplot of 'Sales' vs. 'Volume' for each site:

# create scatterplot
library(ggplot2)
ggplot(gas_sales, aes(x = Volume, y = Sales, color = Site)) +
  geom_point() +
  labs(title = 'Sales vs. Volume by Site')

The scatterplot shows that there is a positive relationship between volume of gas sold and convenience store sales at both sites. However, 'Site 2' has a higher volume of gas sold and generally higher sales than 'Site 1'. Therefore, it is likely that the observed difference in sales between the two sites is partially or fully explained by differences in traffic (i.e., volume of gas sold).

In conclusion, while a two-sample t-test on the sales data suggests a significant difference in performance between the two service stations, this analysis should be interpreted with caution due to potential confounding by differences in traffic. To better understand the relative performance of the two sites, it would be important to consider additional factors that may influence sales (e.g., location, demographics of customers, etc.).