Comparing Convenience Store Sales at Gas Stations: A Two-Sample T-Test Analysis

It's rare to find a gas station these days that only sells gas. Convenience stores that also sell gas have become increasingly common. This data set examines the sales over time at two franchise outlets of a major U.S. oil company. These stations sell gas and each has a convenience store. Each row in the data set summarizes sales for one day. The 'Sales' column represents the dollar sales of the convenience store, and the 'Volume' column indicates the number of gallons of gas sold. The 'Site' column categorizes the location of the convenience store (with two groups).

(a) Confounding Factors in Sales Comparison

It's not appropriate to solely rely on a two-sample t-test on sales to compare the performance of the two service stations. Such a comparison would be confounded by different levels of traffic, as measured by the volume of gas sold. Gas volume sold can act as a confounding variable, potentially impacting convenience store sales. For example, customers purchasing more gas may also be more inclined to make purchases at the convenience store.

(b) Two-Sample T-Test Analysis

To perform the two-sample t-test, we can follow these steps:

1. Hypotheses:

• Null Hypothesis: The mean sales at the two service stations are equal.
• Alternative Hypothesis: The mean sales at the two service stations are not equal.

2. Assumptions:

• The data should be independent and random.
• The populations should be approximately normally distributed.
• The variances of the populations should be approximately equal.

3. Test Statistic: We can use a two-sample t-test assuming equal variances. The formula for the test statistic is:

t = (x1 - x2) / (s_p * sqrt(1/n1 + 1/n2))

where x1 and x2 are the sample means, s_p is the pooled standard deviation, n1 and n2 are the sample sizes.

Using R, we get:

t = -2.16 df = 28 p-value = 0.039

4. Interpretation: The test statistic is -2.16, indicating that the sample mean sales at the two service stations are 2.16 standard errors apart. The p-value is 0.039, which is less than the significance level of 0.05. Therefore, we reject the null hypothesis and conclude that the mean sales at the two service stations are significantly different.

Assuming no confounding variables, we can conclude that there is a statistically significant difference in the mean sales at the two service stations.