You are analyzing customer data and want to segment users into low-, medium-, and high-engagement groups based on monthly article downloads in a research platform. In a sample of 900 customers, the low-engagement segment has 300 customers with mean annual renewal spend of 420 and standard deviation 110, the medium-engagement segment has 360 customers with mean 510 and standard deviation 130, and the high-engagement segment has 240 customers with mean 610 and standard deviation 150. You want to know whether these segments are meaningfully different for analysis.
How would you statistically evaluate whether this segmentation is useful, and based on the data, do the customer segments differ significantly in mean annual renewal spend?