Two-Sample t-Test: Comparing Daily Sales Across Retail Store Formats

The Scenario

FreshMart Retail Group operates 82 stores across the southwestern United States under two distinct store formats: Express stores (small-format, neighborhood convenience locations averaging 3,000 sq ft) and Superstores (large-format, full-range locations averaging 18,000 sq ft). The regional VP of Operations has noticed conflicting reports from store managers — Express store managers claim their revenue-per-square-foot rivals the Superstores, while Superstore managers argue their absolute daily sales figures are significantly higher. With the company planning to invest $45 million in 12 new store openings next fiscal year, leadership needs clarity: is there a statistically meaningful difference in average daily sales between the two formats, or are the observed differences just random variation?

The Statistical Challenge

The analytics team has pulled 40 randomly sampled days of sales data from each store format — 40 observations for Express stores and 40 for Superstores — capturing daily total revenue in USD. While the raw averages suggest Superstores sell more per day, daily sales figures are inherently noisy: they fluctuate due to weekday vs. weekend patterns, local demographics, promotions, and seasonal effects. The core question is whether the difference in average daily sales is large enough to be statistically significant, or whether it could plausibly be explained by this natural variability. As the data analyst on this project, you will apply a two-sample independent t-test to formally answer this question with a quantified level of confidence.

What's at Stake

The outcome of this analysis directly shapes FreshMart's capital allocation strategy. If Superstores generate significantly higher daily sales, the investment case for large-format expansion is strengthened. If the difference is statistically negligible, the company may be better served doubling down on lower-cost Express locations with faster rollout timelines. Your statistical conclusion — backed by a p-value, test statistic, and plain-language interpretation — will be presented directly to the VP of Operations to inform the $45M investment decision.