The manager of a marketing research company wants to assess whether the customers' preference for any of the four brands of Ice-cream: A, B, C, and D is independent of their flavours: Vanilla, Chocolate, and Strawberry. A random sample of 527 customers was asked about their choice and the data are given in the following table:

A B C D Vanilla 28 90 20 35 Chocolate 86 45 23 22 Strawberry 37 30 27 84 (a) Calculate the proportion of customers preferring Vanilla flavours. (b) Calculate the proportion of customers preferring brand B (c) What proportion of customers does prefer chocolate flavour of brand A? (d) Which brand with Strawberry flavour has the highest proportions of customers? Justify your answer. (e) Test the hypothesis that the customers' preference for any of the four brands of ice-cream is independent of their flavour. Use 5% significance level.