(10 marks)

A marketing firm that markets refrigerators is interested in studying consumer behavior in the context of purchasing a particular brand of refrigerator. It wants to know, in particular, whether the income-level of the consumers influences their choice of refrigerator brand. Currently there are three brands available in the marketplace. Brand A is a premium brand, Brand B is a more moderately priced brand, and Brand C is the most economical brand.

A representative stratified random sampling procedure was adopted covering the entire market using income as the basis of selection. Income was classified into three categories: lower, middle and high. A sample of 200 consumers participated in this study and produced the following data:

Brand A Brand B Brand C

Lower. 20 30 50

Middle 20 25 15

High 10 15 15

At the 5% significance level, can it be concluded that there is a relationship between income-level and brand preference? Formulate and test the appropriate hypotheses. Use the critical value approach. Clearly state and explain your conclusion within the context of the question.