Use Monte Carlo simulation for estimating type I error rate of chi-square test of independence. Consider two categorical variables, say X and Y . Suppose X represents race/ethnicity with four categories (White, Black, Hispanic, and others) and Y represents a certain disease status (Yes/No). A chi-square test statistic may be used to test association between these two variables. Its asymptotic null distribution is chi-square, however, this distribution may not be valid in some situations. In particular, even though a 5% level (referred as nominal level) test is used for inference, the actual type I error rate may be quite different from 5%. Thus, it is desirable to estimate the actual type I error rate of this test statistic by Monte Carlo simulation. Vary n to be 20, 50, 100, and 500. For simulating X, use the following proportions: White: 62%, Black: 13%, Hispanic: 18%, and Others: 7%. For simulating Y , assume that the prevalence of the disease in the population is 25%. For number of replications (N), use the minimum value of N, which ensures that the SE of the estimated type I error rate is no more than 0.005 (justify your choice). Compare the estimated type I error rate with the nominal rate of 5%. The starting seed value, is 3000.