A large supermarket carries four qualities of ground beef. Customers are believed to purchase these four varieties with probabilities of 0.14, 0.27, 0.13, and 0.46, respectively, from the least to most expensive variety. A sample of 512 purchases resulted in sales of 48, 152, 90, and 222 of the respective qualities. Does this sample contradict the expected proportions?
a.Find the χ2 statistic.