NAMELAB is a San Francisco-based company that uses linguistic analysis and computers to invent catchy names for new products. The company is credited with the invention of Acura, Compaq, Sentra, and other names of successful products. Naturally, statistical analysis plays an important role in choosing the final name for a product.
In choosing a name for a compact disk player, NAMELAB is considering four names and uses analysis of variance for determining whether all four names are equally liked, on average, by the public.
The results include n1 = 32, n2 = 30, n3 = 28, n4 = 41, SSTR = 4,537, and MSE = 412. Are all four names approximately equally liked, on average? What is the approximate p-value?