Chi-square test for independence of attributes.
An investment portfolio manager categorized her investors as having moderate, medium or high incomes, based on their records. She then rates their overall degree of investment risk from an analysis of the profile of their investments. Counts for investor income and investment risk for 1094 randomly selected investors from one of her investment funds are given in Table 1. She is interested to see if a relationship exists between declared income level and degree of investment risk.
(i) Explain why a x2 test of the resulting contingency table is appropriate for such an investigation.
(ii) Under take a suitable x2 test to establish if there is any evidence, at the 5% significance level, that investment risk depends on level of income.