The average cost of coffee in three cities was calculated, on the basis of samples sized 10 in each city. The averages were, respectively, 10.5, 9.1, 8.3, and $\sum_{i=1}^{3} \sum_{j=1}^{10} (x_{ij} - \bar{x_i})^2 = 2.7$. Applying a test of analysis of variance, verify whether the data confirms a relationship between the city and price levels. What are the necessary assumptions allowing the use of ANOVA?